Answer the following questions about the function whose derivative is given below.
a. What are the critical points of​ f?
b. On what open intervals is f increasing or​ decreasing?
c. At what​ points, if​ any, does f assume local maximum or minimum​ values?

The perimeter of the rhombus in this problem is given as follows:

19.8 units.

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

The diagonal length can be obtained as follows:

RU + UT = 7.

Applying the Pythagorean Theorem, the side length is obtained as follows:

x² + x² = 7²

2x² = 49

[tex]x = \sqrt{\frac{49}{2}}[/tex]

x = 4.95.

Then the perimeter is given as follows:

P = 4 x 4.95

P = 19.8 units.

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The minimum amount of cholesterol is 350 units.

To minimize cholesterol intake while meeting the daily supplement requirements, we need to find the optimal amounts of foods I and II to consume. Let's denote the amount of food I as x ounces and the amount of food II as y ounces.

We have the following constraints:
- The total supplement of the two foods must be at most 22 ounces: x + y ≤ 22
- The daily vitamin C requirement is at least 380 units: 76x + 38y ≥ 380
- The daily vitamin E requirement is at least 170 units: 10x + 20y ≥ 170

To minimize cholesterol intake, we need to minimize the amount of cholesterol from both foods. Food I contains 10 units of cholesterol per ounce, so the cholesterol from food I is 10x. Food II contains 16 units of cholesterol per ounce, so the cholesterol from food II is 16y. Therefore, the total cholesterol is 10x + 16y.

Now, let's solve this problem using linear programming:

Step 1: Rewrite the constraints in terms of x and y:
x + y ≤ 22
76x + 38y ≥ 380
10x + 20y ≥ 170

Step 2: Graph the feasible region determined by these constraints.

Step 3: Identify the corner points of the feasible region.

Step 4: Substitute the corner points into the objective function 10x + 16y and find the minimum value.

After performing these steps, we find that the minimum amount of cholesterol is 350 units.

The values for x and y that correspond to the minimum cholesterol intake may vary, so it is important to verify the optimal solution by substituting the values into the constraints to ensure they satisfy all the requirements.

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Answer: The prime factorization of 15 is 3x5.

The area of the parallelogram is  189 square units

First, we have the determine the length of the base and height.

The distance between the lines x = 9 and f(x) = 9 + 2x is the height

We have that the line parallel to f(x) passes through (4, 11)

The equation in point-slope form is;

y - 11 = 2(x - 4

y = 2x + 3

Substitute x = 9 in the equation,  y = 2x + 3.

y = 2(9) + 3 = 21

The  points are then (9, 21) and (9, 0).

The distance between the y-axis and the line x = 9 is the base.

Base = 9 units.

The formula for calculating area of a parallelogram is given by ;

= base × height

= 9 × 21

= 189 square units.

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Answer:

B

Step-by-step explanation:

Yes, because for each input there is exactly one output. You can have two of the same x values but you cannot have 2 of the same y values. if you have two of the same y values, it is not a function as it doesn't pass the vertical line test.

Answer:

The table represents a nonlinear function because the rate is not constant.

Step-by-step explanation:

As shown in the picture below, the x side of the table has the same rate of change of +1. However, due to the fact that the y side does not have the same rate of change, +6 and +3, the table represents a non linear function. If the rate on the y side of the table were all the same, then this would be a Linear function.

The range of the inverse of the function is [2, ∝)

From the question, we have the following parameters that can be used in our computation:

f(x) = √x - 2

Set the radicand greater tahn or equal to 0

So, we have

x - 2 ≥ 0

When evaluated, we have

x ≥ 2

This means that

[2, ∝)

Hence, the range of the inverse of the function is [2, ∝)

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a. The initial velocity of the marble is 0 cm/s.

b. The marble is rolling at a speed of 80 cm/s at 4 seconds.

c. The velocity is 50 cm/s at approximately t = 2√2 - 1 seconds.

d. The marble is rolling at a speed of 90 cm/s when it is 90 cm from its starting point at t = 9 seconds.

e. lim s(t) as t approaches infinity is 100 cm and lim v(t) as t approaches infinity is 0 cm/s; the model may not be valid for large values of t as it assumes the marble is rolling up an inclined plane without considering other factors such as friction.

a. To find the initial velocity of the marble, we need to calculate the limit of the function s(t) as t approaches 0:

lim (t->0) s(t) = lim (t->0) (100t / (t + 1))

By substituting 0 into the expression, we get:

lim (t->0) (0 / (0 + 1)) = 0 / 1 = 0.

Therefore, the initial velocity of the marble is 0 cm/s.

b. To find the speed of the marble at time 4 seconds, we substitute t = 4 into the expression for s(t):

s(4) = 100(4) / (4 + 1) = 400 / 5 = 80 cm/s

The marble is rolling at a speed of 80 cm/s at 4 seconds.

c. To find the time at which the velocity is 50 cm/s, we set s'(t) (the derivative of s(t)) equal to 50 and solve for t:

s'(t) = 50

[tex](100 / (t + 1))^2 = 50[/tex]

100 / (t + 1) = ±√50

100 = ±√50(t + 1)

±√50(t + 1) = 100

t + 1 = 100 / ±√50

t + 1 = ±2√2

Since time cannot be negative, we take t + 1 = 2√2:

t = 2√2 - 1

The velocity is 50 cm/s at approximately t = 2√2 - 1 seconds.

d. To find the speed of the marble when it is 90 cm from its starting point, we need to solve the equation s(t) = 90 for t:

100t / (t + 1) = 90

100t = 90(t + 1)

100t = 90t + 90

10t = 90

t = 9

The marble is rolling at a speed of 90 cm/s when it is 90 cm from its starting point, which occurs at t = 9 seconds.

e. The limit of s(t) as t approaches infinity (lim s(t) as t->∞) is calculated by considering the dominant term in the numerator and denominator:

lim (t->∞) (100t / (t + 1))

≈ lim (t->∞) (100t / t)

= lim (t->∞) 100

= 100

Therefore, lim s(t) as t approaches infinity is 100 cm.

Similarly, the limit of v(t) (velocity) as t approaches infinity (lim v(t) as t->∞) can be found by taking the derivative of s(t) and evaluating the limit:

[tex]v(t) = s'(t) = 100 / (t + 1)^2[/tex]

lim (t->∞) v(t) = lim (t->∞) (100 / [tex](t + 1)^2)[/tex]

≈ lim (t->∞)[tex](100 / t^2)[/tex]

= lim (t->∞) [tex](100 / t^2)[/tex]

= 0.

The limit of v(t) as t approaches infinity is 0 cm/s.

As for the validity of the model for large values of t, it is important to note that the given model assumes that the marble is rolling up an inclined plane.

However, without further information about the nature of the inclined plane (e.g., its slope, frictional forces), it is difficult to determine the accuracy.

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The periodic payment required to accumulate a sum of $50,000 over 8 years with an interest rate of 6% compounded semiannually is approximately $79,466.27.

To find the periodic payment required to accumulate a sum of S dollars over t years with interest earned at the rate of r% per year compounded m times a year, we can use the formula for the future value of an ordinary annuity:

R = S / (((1 + r/m)^(m*t)) - 1)

Given the values:

S = 50,000 (sum to accumulate)

r = 6 (interest rate in percentage)

t = 8 (number of years)

m = 2 (compounding frequency per year)

Substituting these values into the formula, we get:

R = 50,000 / (((1 + 6/100/2)^(2*8)) - 1)

Simplifying further:

R = 50,000 / (((1 + 0.06/2)^(16)) - 1)

R = 50,000 / (((1.03)^(16)) - 1)

Using a calculator, we find that (1.03)^16 is approximately 1.62989494.

R = 50,000 / (1.62989494 - 1)

R = 50,000 / 0.62989494

R ≈ $79,466.27

Therefore, the periodic payment required to accumulate a sum of $50,000 over 8 years with an interest rate of 6% compounded semiannually is approximately $79,466.27.

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Answer:

380 seconds

Step-by-step explanation:

Convert 6 minutes to seconds by multiplying 6 times 60, because there are 60 seconds per minute.
6 x 60 = 360

Now add the 20 seconds.
360 + 20 = 380

6 minutes and 20 seconds are equal to 380 seconds.

The range of the rational function is the set of all real numbers larger than 60 but less than 560, therefore;

Range; [60, 560]

A rational function, f(x) is a function that can be expressed in the form f(x) = p(x)/q(x), where the functions p(x) and q(x) are polynomial functions.

The initial fee charged by the cell phone company = $500

The monthly charge after purchase = $60

The total cost of owning the cell phone = $500 + $60·t

The average monthly cost of owning a cell phone is therefore;

C(t) = (500 + 60·t)/t

The range of the function is the set of all possible values o C(t), which can be frond from the limit of the function, as follows;

[tex]\lim\limits_{x\to\infty}C(t) = \lim\limits_{x\to\infty}\frac{500 + 60\cdot t}{t} = \lim\limits_{x\to\infty}(\frac{500 }{t} + 60)[/tex] = 60

The limit of the average monthly cost indicates that the range of the function approaches $60 as t approaches infinity.

When t = 1, we get; C(1) = (500 + 60 × 1)/1 = 560

The range of the function is therefore, the set of all real numbers, larger than $60 but less than $560

The range of the function is therefore; [60, 560]

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The postulate or theorem that proves that two triangles are congruent if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle. Of the above choices, only ASA satisfies this condition. So the answer is (C).

ASA Congruence Theorem explains that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

This theorem is a part of triangle congruence criteria in Euclidean geometry. It states that if two angles and the included side of one triangle are equal to the corresponding two angles and included side of another triangle, then the two triangles are congruent, meaning they have the same shape and size.

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The coefficient of x is -1, indicating that there is one fewer x term compared to the original expression. The constant term is -4, which is the result of subtracting 5 from -9.

To find the difference when subtracting 8x - 5 from 7x - 9, we can use the distributive property to distribute the negative sign to each term in 8x - 5:

(7x - 9) - (8x - 5) = 7x - 9 - 8x + 5

Next, we can combine like terms by adding or subtracting the coefficients of the same variables:

7x - 9 - 8x + 5 = (7x - 8x) + (-9 + 5) = -x - 4

Therefore, the expression that represents the difference when 8x - 5 is subtracted from 7x - 9 is -x - 4.

In this expression, the coefficient of x is -1, indicating that there is one fewer x term compared to the original expression. The constant term is -4, which is the result of subtracting 5 from -9.

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the answer for the question that you are asking will possibly be 17

Answer:

-3[tex]x^{6}[/tex] + 5

Step-by-step explanation:

3 - 3[tex]x^{6}[/tex] + 2 = ?

-3[tex]x^{6}[/tex] + 5

So, the answer is -3[tex]x^{6}[/tex] + 5

The best description of the fees he is charged for renting or the cost per mile would be = He is charged an initial rate of $55.60 for renting the van. That is option E.

To determine the best description for the cost per mile, the following steps needs to be taken as follows:

The average cost per mile he was given for renting the trucks would be calculated by addition of the total cost divided by the miles driven.

Total cost = 55.60+53.22+51.16+54.97+52.38/

= 267.33

Total miles driven = 80+46+23+71+34 = 254

The average = 267.33/254 = 1.1

Therefore since the initial price given = $55.60, the best statement = He is charged an initial rate of $55.60 for renting the van

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Answer:

x = 4 , ∠ AXC = 150°

Step-by-step explanation:

∠ 1 and ∠ 2 form the angle AXC , that is

∠ AXC = ∠ 1 + ∠ 2 , then

6(6x + 1) = 102 + 10x + 8

36x + 6 = 10x + 110 ( subtract 10x from both sides )

26x + 6 = 110 ( subtract 6 from both sides )

26x = 104 ( divide both sides by 26 )

x = 4

Then by substituting x = 4

∠ AXC = 6(6x + 1) = 36x + 6 = 36(4) + 6 = 144 + 6 = 150°

a. The distribution of X is X ~ N(68, 14).

b. The corresponding area to the right of 0.9286, which is approximately 0.1772.

c. The longest amount of time a patron can spend and still receive the discount is approximately 48.5654 minutes.

d. The Inter Quartile Range (IQR) for time spent at the hot springs is approximately 21.373 minutes.

a. The distribution of X is X ~ N(68, 14), where X represents the amount of time a person spends at Grover Hot Springs, 68 is the mean, and 14 is the standard deviation.

b. To find the probability that a randomly selected person stays longer than 81 minutes, we need to calculate the area under the normal curve to the right of 81.

Using the z-score formula: z = (x - μ) / σ, where x is the value (81), μ is the mean (68), and σ is the standard deviation (14).

Plugging in the values, we have z = (81 - 68) / 14 = 0.9286.

Using a standard normal distribution table or a calculator, we can find the corresponding area to the right of 0.9286, which is approximately 0.1772.

c. To find the longest amount of time a patron can spend at the hot springs and still receive the discount, we need to find the value that corresponds to the lowest 8% of the distribution.

Using a standard normal distribution table or a calculator, we can find the z-score that corresponds to the 8th percentile, which is approximately -1.4051.

Using the z-score formula, we can calculate the longest amount of time: x = μ + z [tex]\times[/tex] σ = 68 + (-1.4051) [tex]\times[/tex] 14 = 48.5654 minutes.

Therefore, the longest amount of time a patron can spend and still receive the discount is approximately 48.5654 minutes.

d. The Inter Quartile Range (IQR) is a measure of the spread of the data and represents the range between the first quartile (Q1) and the third quartile (Q3).

To find Q1 and Q3, we can use the z-score formula and the standard normal distribution table.

For Q1, we find the z-score corresponding to the 25th percentile, which is approximately -0.6745.

Using the formula Q1 = μ + z [tex]\times[/tex] σ, we have Q1 = 68 + (-0.6745) [tex]\times[/tex] 14 = 57.053.

Therefore, Q1 is approximately 57.053 minutes.

For Q3, we find the z-score corresponding to the 75th percentile, which is approximately 0.6745.

Using the formula Q3 = μ + z [tex]\times[/tex] σ, we have Q3 = 68 + (0.6745) [tex]\times[/tex] 14 = 78.426.

Therefore, Q3 is approximately 78.426 minutes.

Finally, we can calculate the IQR by subtracting Q1 from Q3: IQR = Q3 - Q1 = 78.426 - 57.053 = 21.373 minutes.

Therefore, the Inter Quartile Range (IQR) for time spent at the hot springs is approximately 21.373 minutes.

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Answer:

To estimate the distance the train traveled in the first 20 seconds using four strips of equal width, follow these steps:

a) Calculate the average velocity for each strip by finding the average height of each strip.

b) Multiply the average velocity of each strip by the width (time) of each strip to obtain the distance covered by each strip.

c) Add up the distances covered by each strip to find the estimated total distance traveled in the first 20 seconds.

Regarding part b), to determine if the estimate is an overestimate or an underestimate, we need to analyze the graph. If the graph shows that the velocity increases during the 20-second period, then the estimate will be an underestimate because the actual distance covered would be greater than the estimation based on a constant velocity assumption. On the other hand, if the graph shows that the velocity decreases during the 20-second period, then the estimate will be an overestimate since the actual distance covered would be less than the estimation based on a constant velocity assumption.

Without seeing the graph, it's difficult to provide a definitive answer.

(3a) The equation that can be used to determine the cost, C is C = 2.55 + 1.85x.

(3b) The cost of 3 miles taxi ride is $8.1.

(3a) The equation that can be used to determine the cost, C is calculated by applying the following equation as follows;

C = f + nx

where

C = 2.55 + 1.85x

(3b) The cost of 3 miles taxi ride is calculated as follows;

C = 2.55 + 1.85x

where;

C = 2.55 + 1.85 (3)

C = $8.1

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The statement about the zeros of function g is that they are located at x = 5 + √2 and x = 5 - √2.

When the vertex of function f is moved 4 units to the right and 2 units down, the equation of function g can be represented as g(x) = -(x-5)^2 + 2.

To determine the statement about the zeros of function g, we need to find the x-values where g(x) equals zero.

Setting g(x) = 0 and solving for x:

[tex]0 = -(x-5)^2 + 2[/tex]

Adding (x-5)^2 to both sides:

[tex](x-5)^2 = 2[/tex]

Taking the square root of both sides (considering both positive and negative roots):

x - 5 = ±√2

Adding 5 to both sides:

x = 5 ± √2

Therefore, the zeros of function g are x = 5 + √2 and x = 5 - √2.

In summary, the statement about the zeros of function g is that they are located at x = 5 + √2 and x = 5 - √2.

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Answer:im not sure

Step-by-step explanation:

your picture is not so clear can you upload again

Inferences about the interaction between Anna and Mrs. Morgan are supported by the information in paragraphs 7 and 8 are as follows: Mrs. Morgan is not very patient with Anna and is trying to get rid of her.Mrs. Morgan thinks Anna is lying and is not telling the truth.

Mrs. Morgan appears to be strict and unkind towards Anna, as well as being skeptical about her intentions. She is not really interested in Anna's concerns and is rather impatient and dismissive, trying to get rid of her as soon as possible. Additionally, Mrs. Morgan doesn't believe Anna, thinking she is lying and hiding something from her.

This suggests that Mrs. Morgan might not be a trustworthy person and has a negative impression of Anna without even knowing her well.

The textual evidence used to support these inferences is the description of Mrs. Morgan's tone and behavior towards Anna as well as her verbal responses, such as the abruptness of her question about the purse and her insistence on Anna leaving.

These actions suggest that Mrs. Morgan is not open to listening to Anna's story and is only interested in getting her out of the way, as well as indicating that she doesn't believe Anna's story.

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Replacement cost of the minibus in 4 years' time, considering the trade-in of the old minibus, is R9,411.70.

1. Calculate the depreciation of the minibus over 4 years:

  Depreciation = Original cost * (1 - Rate of depreciation) Number of years

  Depreciation = R241,000 * (1 - [tex]0.22)^4[/tex]

  Depreciation = R241,000 * [tex]0.78^4[/tex]

  Depreciation ≈ R91,073.17

2. Calculate the remaining value of the minibus after 4 years:

  Remaining value = Original cost - Depreciation

  Remaining value = R241,000 - R91,073.17

  Remaining value ≈ R149,926.83

3. Calculate the inflated cost of a new minibus in 4 years:

  Inflated cost = Original cost * (1 + Rate of inflation) Number of years

  Inflated cost = R241,000 * (1 + [tex]0.15)^4[/tex]

  Inflated cost = R241,000 * [tex]1.15^4[/tex]

  Inflated cost ≈ R421,731.04

4. Calculate the replacement cost by subtracting the remaining value and adding the inflated cost:

  Replacement cost = Remaining value + Inflated cost

  Replacement cost = R149,926.83 + R421,731.04

  Replacement cost ≈ R571,657.87

5. Calculate the trade-in value by subtracting the depreciation from the replacement cost:

  Trade-in value = Replacement cost - Depreciation

  Trade-in value = R571,657.87 - R91,073.17

  Trade-in value ≈ R480,584.70

6. Therefore, the replacement cost of the minibus in 4 years' time, considering the trade-in, is approximately R480,584.70.

For the second question:

1. Determine the number of months until the first payment is made:

  Number of months = 4 years * 12 months/year - 3 months

  Number of months = 48 months - 3 months

  Number of months = 45 months

2. Use the formula for the future value of a series of payments to calculate the required monthly payment:

  Monthly payment = (Future value * Interest rate) / ((1 + Interest rate) Number of periods - 1)

  Monthly payment = (Replacement cost * Monthly interest rate) / ((1 + Monthly interest rate) Number of months - 1)

  Monthly payment = (R480,584.70 * 0.086/12) / ((1 + [tex]0.086/12)^4^5[/tex] - 1)

  Monthly payment ≈ R9,411.70

3. Therefore, the required monthly payment to the sinking fund for the purchase of a new minibus in 4 years' time, with the first payment made three months after the original bus was purchased, is approximately R9,411.70.

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Answer:

1.255 seconds

Step-by-step explanation:

We can use the formula:

time = distance ÷ speed

to find the driver's time. Here, the distance is 200 miles and the speed is 159.5 miles per hour. Substituting these values into the formula, we get:

time = 200 miles ÷ 159.5 miles per hour

time = 1.255 seconds

The appropriate shape to model each section of the tower are the cone and the cylinder.

The approximate surface area of each shape would be =

For cone = 1,041.27m²

For cylinder = 3,543.72m².

The first shape is a cone and the formula for the surface area = A = πr(r+√h²+r²)

where;

Radius = 24/2 = 12

height = 10m

Area = 1,041.27m²

For cylinder:

A = 2πrh+2πr²

where:

r = 12m

h = 35m

A = 3,543.72m²

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The calculated percentage error with the assumed answer of 10%

To find the percentage error in actual weights, we can use the formula:

Percentage Error = [(|Measured Value - Expected Value|) / Expected Value] * 100%

In this case, the expected weight is 4 ounces. Let's assume the measured value is 10% off from the expected value. So the measured value would be:

Measured Value = Expected Value + (10% of Expected Value)

              = 4 ounces + (10/100) * 4 ounces

              = 4 ounces + 0.4 ounces

              = 4.4 ounces

Now we can calculate the percentage error:

Percentage Error = [(|4.4 ounces - 4 ounces|) / 4 ounces] * 100%

               = [(0.4 ounces) / 4 ounces] * 100%

               = (0.4/4) * 100%

               = 0.1 * 100%

               = 10%

Comparing the calculated percentage error with the assumed answer of 10%, we can see that they are the same.

The percentage error represents the deviation from the expected value as a percentage of the expected value itself. In this case, it indicates that the actual weights deviate by 10% from the expected weight of 4 ounces. The calculated percentage error with the assumed answer of 10%

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Answer:

After 24 hours 24 thousand views are predicted.

Step-by-step explanation:

To find the number of times the video is predicted to be viewed after 24 hours, we evaluate f(24) for the function f(t)=7000/1+35000e−0.2t

f(24)=7000/1+35000e^(−0.2⋅(24))

f(24)=7000/1+35000e^−4.8

f(24)≈24.21800522

After 24 hours, 24 thousand views are predicted.

The number of views that the video would get after 24 hours based on the function is 24 thousand

An exponential function is a mathematical function of the form:

f(x) =[tex]a^x[/tex]

where "a" is a positive constant called the base, and "x" is the exponent, representing the power to which the base is raised. The exponent "x" can be any real number, making exponential functions quite versatile in describing a wide range of phenomena.

We have that;

=7000/1+35000[tex]e^{-0.2t[/tex]

Where t = 24 hours

=7000/1+35000[tex]e^{-0.2 * 24[/tex]

= 24

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Answer:

[tex]12000 ( {1 + \frac{.04}{12}) }^{12t} = 17000[/tex]

[tex] {( \frac{301}{300}) }^{12t} = \frac{17}{12} [/tex]

[tex]12t (ln(301) - ln(300) ) = ln(17) - ln(12) [/tex]

[tex]t = \frac{ ln(17) - ln(12) }{12( ln(301) - ln(300) )} = 8.72 \: years[/tex]