The amount of a pollutant (measured as parts per million) in a local lake can be modeled by the function of A(t)=14(2.71)^-.016*t, where t is the number of years since a government program was began to help clean up the lake. About how long will it take for the amount of pollutant to reach 7 parts per million?

Answers

Answer 1

Solving the exponential function, it is found that it will take 43.5 years for the amount of pollutant to reach 7 parts per million.

What is the exponential function for the amount of the substance?

It is given by, after t years:

[tex]A(t) = 14(2.71)^{-0.016t}[/tex]

It will reach an amount of 7 parts per million when A(t) = 7, hence:

[tex]A(t) = 14(2.71)^{-0.016t}[/tex]

[tex]7 = 14(2.71)^{-0.016t}[/tex]

[tex](2.71)^{-0.016t} = 0.5[/tex]

[tex]\log{(2.71)^{-0.016t}} = \log{0.5}[/tex]

[tex]-0.016t\log{(2.71)} = \log{0.5}[/tex]

[tex]t = -\frac{\log{0.5}}{0.016\log{2.71}}[/tex]

t = 43.5.

More can be learned about exponential functions at https://brainly.com/question/25537936

#SPJ1


Related Questions

My supersonic jet burns 4 gallons of jet fuel in 3 seconds. How many gallons of jet fuel do I need to fly for an hour?

Answers

The number of gallons of Jet fuel that is needed to fly for an hour is; 14400 gallons

How to solve simple Algebra?

We are given;

Number of gallons burned = 4 gallons

Time to burn 4 gallons = 3 seconds

Now, for 1 hour there are 3600 seconds and so;

Number of gallons that is burnt in 3600 seconds = 3600 * 4

Number of gallons that is burnt in 3600 seconds = 14400 gallons

Read more about Algebra at; https://brainly.com/question/4344214

#SPJ1

Select the graph for the solution of the open sentence. Click until the correct graph appears.

3|x| > 6

I would really appreciate the help!:)

Answers

The solution of the inequality will be x > 2 and x < -2. And the graph is drawn below.

What is inequality?

Inequality is defined as an equation that does not contain an equal sign.

The inequality is given below.

3|x| > 6

By solving the equation, we have

|x| > 2

x > 2

x < -2

Then the graph will be drawn.

More about the inequality link is given below.

https://brainly.com/question/19491153

#SPJ1

Help please I will do anything

Answers

Answer:

? = 12

Step-by-step explanation:

[tex]\frac{7}{12} +\frac{10}{12} =\frac{7+10}{12} =\frac{17}{12}[/tex]

[tex]\frac{17}{12} =\frac{12}{12} +\frac{5}{12} =1+\frac{5}{12} =1\frac{5}{12}[/tex]

Hope this helps

Graph the function f(x) = x+4 -1.

Answers

This can be simplified to [tex]f(x)=x+3[/tex], and is thus a line with a slope of 1 and a y-intercept of 3.

Sara purchased a porcelain sculpture that is in the shape of a square pyramid. The slant height is 6.1 inches and the base 6.4 inches. Find the surface area. Round to the nearest tenth.

Answers

The surface area of the square pyramid will be 78.08 square inches.

What is surface area?

The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called the surface area.

Given that:-

Sara purchased a porcelain sculpture that is in the shape of a square pyramid. The slant height is 6.1 inches and the base is 6.4 inches. The surface area will be.

The surface area of the square pyramid will be calculated by the formula:-

[tex]SA = P\times\dfrac{l}{2}[/tex]

[tex]SA = 25.6\times \dfrac{6.1}{2}[/tex]

SA = 78.08 square inches

Therefore the surface area of the square pyramid will be 78.08 square inches.

To know more about a surface area follow

https://brainly.com/question/23773586

#SPJ1

The frequency table shows the results of a survey asking people how many
hours they spend online per week. On a piece of paper, draw a histogram to
represent the data. Then determine which answer choice matches the
histogram you drew.
Hours online Frequency
5
8
10
9
7
0-3
4-7
8-11
12-15
16-19

Answers

Based on the frequency table given, The option that closely matches the histogram I drew is option C but the last one suppose to be 7 and not 6.

What is the histogram about?

Hours online   Frequency

5                           0-3

8                          4-7

10                         8-11

9                          12-15

7                           16-19

Note that in the image attached, you can see how the Hours online were said to be matched with the  Frequency.

So since option A and B was not shown to see which matches the option,  i can say option c is closest but if look at my own image, you can use it to find the right one.

Learn more about frequency from

https://brainly.com/question/254161

#SPJ1

In a certain town, the ratio of the number of children to the number of adults is 3 to 7. What percent of the town’s population are adults?

Answers

Answer:

70%

Step-by-step explanation:

If 3 child and 7 adult is in the town, then there are total 10 people. 7 ÷ 10 is equal to 0.7, which is 70%.

if 50 grams of sweets cost 250 rupees find the cost of 380 grams of sweets. ​

Answers

Cost of 380 gram of sweets = (2.1/50) * 380 = $15.96

What is the volume of the complex figure

Answers

The volume of the given figure is 104 m³.

We need to find the volume of the given figure.

What is volume?

Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface.

Divide the given figure into two convenient cuboids. That is one with dimensions length=4 m, breadth=4 m and height=3 m. Another with length=4 m,  breadth=7 m and height=2 m.

We know that, the volume of cuboid =l×b×h cubic units.

Now, the volume of cuboid=4×4×3=48 m³ and the volume of another

cuboid=4×7×2=56 m³.

The volume of the given figure=48+56=104 m³.

Therefore, the volume of the given figure is 104 m³.

To learn more about the volume visit:

https://brainly.com/question/1578538.

#SPJ1


Which of the following statements must be true about this diagram? Check
all that apply.

A. mz2+ mz3 = mz4
B. mz1+ m2 2 = m/3
C. m23 is greater than m<2
D. m24 is greater than mz1
E. mz1+mz2 = mz4
F. mz4 is greater than m<2

Answers

Answer:

D, E, F is the answer.

Step-by-step explanation:

From the diagram:-

m∠ 4 is greater than m∠ 1m∠ 4 is greater than m∠ 2m∠ 1 + m∠ 2 = m∠ 4

Therefore, D, E, F.

-------------------------------

Please help! I don't know how to do slopes.

Answers

The slope of the given line in  the image is -4 , Option A is the answer.

What is the equation of a straight line ?

The equation of the straight line is given by

y =mx +c ,

Where m is the slope , C is the intercept

The line is passing through the point

(-1,8)  ,(2,-4)

The slope is given by

m = (y₂-y₁) /(x₂-x₁)

m  = (-4 - 8 )/(2 +1)

m = -12/3

m = -4

Therefore the slope of the given line in  the image is -4 , Option A is the answer.

To know more about Straight Line equation

https://brainly.com/question/959487

#SPJ1

What is the solution to the following equation?
-3+x= -8

A. x = -5
B. x=5
C. x = 11
D. x=-11

Answers

x = -5.

Add 3 to each side, -8 + 3 = -5

Answer:

[tex]\mathsf {A. x = -5}[/tex]

Step-by-step explanation:

[tex]\implies \mathsf {-3 + x = -8}[/tex]

[tex]\implies \mathsf {x = -8 + 3}[/tex]

[tex]\implies \mathsf {x = -5}[/tex]

The vertices of a trapezoid are points (0,x), (0,0), (y,0), and (z,x). Find the area in terms of x, y, and z.

I put 1/2x (y+z), I just want to make sure! thank you.

Answers

Your answer is correct. The two "bases" of the trapezoid are the line segments (0, 0)-to-(y, 0) and (0, x)-to(z, x), with lengths y and z, respectively. Then the average of the bases is [tex]\frac{y+z}2[/tex]. (We know they're the bases because the line segments are parallel.)

We multiply this by the height, which is given by the length of the line segment (0, 0)-to-(0,x), or x.

Hence the area is

[tex]\dfrac{x(y+z)}2[/tex]

(which is identical to what you have).

The May bank statement for Rental shows a balance of $6,000, but the balance per books shows a cash balance of $8,000. Other information includes: 1. A check for $190 to pay the electric bill was recorded on the books as $10. 2. Included on the bank statement was a note collected by the bank for $450 plus interest of $30. 3. Checks outstanding totaled $270. 4. Bank service charges were $60. 5. Deposits in transit were $2,510.

Answers

The adjusted cash Balance is $8060 .

What is Bank Balance ?

The amount of money in a person's account at any given time is the Bank Balance of that person's account.

Unadjusted bank balance       6000

Difference in the electricity bill    -180

Add: Deposit in transit               2510

Less: Outstanding Checks         -270

Adjusted cash balance                8060

So answer is a) $8060

Therefore the adjusted cash Balance is $8060 .

To know more about Bank Balance

https://brainly.com/question/26699275

#SPJ1

A company gives each worker a cash bonus every Friday, randomly giving a worker an amount with these probabilities: $10 - 0.75, $50 - 0.25. Over many weeks, what is a worker's expected weekly bonus?

Answers

The worker's expected weekly bonus is $30.0

How to determine the worker's expected weekly bonus?

The amounts and the probabilities are given as:

x    $10       $50

P(x)  0.75    0.25

The worker's expected weekly bonus is calculated as:

[tex]E(x) = \sum x * P(x)[/tex]

So, we have:

E(x) = $10 * 0.75 + $50 * 0.25

Evaluate the product

E(x) = $17.5 + $12.5

Evaluate the sum

E(x) = $30.0

Hence, the worker's expected weekly bonus is $30.0

Read more about expected values at:

https://brainly.com/question/15858152

#SPJ1

Which of the following is equivalent to the radical expression below when
x>=2?
(√x-2)(√x+9)

Answers

The equivalent expression of [tex](\sqrt x - 2)(\sqrt x + 9)[/tex] is [tex]x + 7\sqrt x - 18[/tex]

How to determine the equivalent equation?

The expression is given as:

[tex](\sqrt x - 2)(\sqrt x + 9)[/tex]

Expand the expression

[tex]x - 2\sqrt x + 9\sqrt x - 18[/tex]

Evaluate the like terms

[tex]x + 7\sqrt x - 18[/tex]

Hence, the equivalent expression of [tex](\sqrt x - 2)(\sqrt x + 9)[/tex] is [tex]x + 7\sqrt x - 18[/tex]

Read more about equivalent expression at:

https://brainly.com/question/2972832

#SPJ1

What is the domain of the function
f(x) = [tex]\sqrt{1/3 x + 2}[/tex]

Answers

The domain of the function is:

D: {x ∈ R | x ≥ -6}

How to get the domain of the function?

Here we have:

[tex]f(x) = \sqrt{(1/3)*x + 2}[/tex]

Remember that the argument of a square root can be only numbers equal to or larger than zero, so the domain of that function is such that:

[tex](1/3)*x + 2 \geq 0[/tex]

Now we can solve that for x.

[tex](1/3)*x + 2 \geq 0\\(1/3)*x \geq -2\\\\x \geq -2*(3/1)\\\\x \geq -6[/tex]

So the domain of the function is:

D: {x ∈ R | x ≥ -6}

If you want to learn more about domains:

https://brainly.com/question/1770447

#SPJ1

Answer:

The domain of the function is:

D: {x ∈ R | x ≥ -6}

what is the volume of this complex figure

Answers

The volume of the given figure is 210 cubic in..

We need to find the volume of the given figure.

What is volume?

Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface.

Divide the given figure into two convenient cuboids. That is one with dimensions length=4 in., breadth=2 in. and height=3 in. Another with length=4 in.breadth=4 in. and height=12 in.

We know that, the volume of cuboid =l×b×h cubic units.

Now, the volume of the cuboid=4×2×3=18 cubic in. and the volume of another

cuboid=4×4×12=192 cubic in.

The volume of the given figure=18+192=210 cubic in.

Therefore, the volume of the given figure is 210 cubic in.

To learn more about the volume visit:

https://brainly.com/question/1578538.

#SPJ1

Given the equation below, which of the following shows the quadratic formula
correctly applied?
2x² -9x+4 =0

Answers

Answer:

Step-by-step explanation:

[tex]x=\frac{-(-9)\pm\sqrt{(-9)^2-4(2)(4)} }{2 \times 2} \\x=\frac{9\pm\sqrt{81-32} }{4} \\x=\frac{9\pm\sqrt{49} }{4} \\x=\frac{9 \pm 7}{4} \\either~x=\frac{9+7}{4} =\frac{16}{4} =4\\or\\x=\frac{9-7}{4} =\frac{2}{4} =\frac{1}{2}[/tex]

Study each of the growing geometrical patterns. Then do the following for each pattern. (I) Give a verbal description of how the pattern is growing. (ii)Set up a table of values.(III) Write down a numerical description for each pattern (you must relate the number of the frame to the number of figures in the frame). (IV) For each pattern, write down a formula that can be used to calculate the number of building blocks in any term. (v) Write down the value of the 10th frame. Use your formula to determine how many building blocks there are in the 100th frame of each growing pattern. M M Δ Δ Δ 2 (6) (6) (8) [40]​

Answers

A description of how the pattern is growing is that the pattern is growing by the addition of two blocks every time.

How to illustrate the pattern?

A numerical description of the pattern is:

1 - 2 blocks.

2 - 4 blocks.

3 - 6 blocks

4 - 8 blocks.

The formula that can be used to calculate the number if building blocks in any term will be 2n. For example, the number of blocks for the 5th term will be:

= 2n = 2 × 5 = 10

The value for the 10th frame will be:

= 2n

= 2 × 10 = 20

The value for the 100th frame will be:

= 2n

= 2 × 100 = 200

Learn more about pattern on:

brainly.com/question/17386984

#SPJ1

Find two positive numbers such that their sum is 60 and their product is a maximum. Select one: O a. 30 and 30 O b. 25 and 35 O c. 1 and 59 O d. 20 and 40​

Answers

Answer:

B: 25 and 35

Step-by-step explanation:

25 product 35 875

A. 30 x 30 = 900
B. 25 x 35 = 875
C. 1 x 59 = 59
D. 20 x 40 = 800

The biggest product is for 30 and 30

If you call one number x the other will be 60 - x
Product = x(60 - x) = 60x - x^2
This is a parabola with roots at 0 and 60
The maximum product is halfway between 0 and 60 ie when x = 30

Please help quickly!!

Answers

Answer:

D

Step-by-step explanation:

A parallelogram ABCD is shown with DC equal to 8 feet and the perpendicular distance between AB and DC equal to 3 over 4 foot. Part A: What is the area of the parallelogram? Show your work. (5 points) Part B: How can you decompose this parallelogram into two triangles? If this parallelogram was decomposed into two triangles, what would be the area of each triangle? (5 points)

Answers

Answer:

6,3

Step-by-step explanation:

hope this helps

the math section in part B shows the equation for the area of a triangle, but this math could be skipped with a similar problem if you just divide the parraellogram by 2. (logic section)

Normal annual capacity for star company is 36,000 machine hours, with fixed factory overhead budgeted as Rs. 16,920 and an estimated variable factory overhead rate of Rs. 2.10 per hour, During October actual production required 2,700 machine hours, with a total factory overhead of Rs. 7,400. Required: Compute: 1) The applied factory overhead 2) The over-or underapplied factory overhead amount for October,

Answers

The applied factory overhead is $6,939 and  the over-or underapplied factory overhead amount for October is $461.

Applied and under applied factory overhead

1. Applied factory overhead:

Predetermine overhead rate=Fixed overhead/Machine hours

Predetermine overhead rate=16,920/36,000

Predetermine overhead rate=0.47

Applied overhead=Machine hours×Rate

Variable=2700×2.10 per hour= $5,670

Fixed=2700×0.47 per hour=$1,269

Total overhead applied=$6,939

($5,670+$1,269)

2. Under applied overhead

Total overhead applied $6,939

Less Total factory overhead   $7,400

Under applied overhead -$461
($6,939-$7,400)

Therefore the applied factory overhead is $6,939 and  the over-or underapplied factory overhead amount for October is $461.

Learn more about  Applied and under applied factory overhead  here:https://brainly.com/question/24170451


#SPJ1

1. What is the length of XU?
X
U
Y
36 in
V
Z
W
23 in

Answers

Answer: 49 in

Step-by-step explanation:

[23 + XU]/2 = 36 [trapezoid midsegment theorem]23 + XU = 72 [multiply both sides by 2]XU = 49 [subtract 23 from both sides]

Given f(x) = 8x+1 2x-9 O As x-00, f(x) → 9; as x → ∞o, f(x) → 9. -> - O As x-00, f(x) O As x-00, f(x) O As x-00, f(x) - - what is the end behavior of the function? ->> -9; as x -4; as x ∞o, f(x) → -9. - ∞o, f(x) → -4. - 4; as x → ∞o, f(x) → 4. -> - Given f ( x ) = 8x + 1 2x - 9 O As x - 00 , f ( x ) → 9 ; as x → ∞o , f ( x ) → 9 . - > - O As x - 00 , f ( x ) O As x - 00 , f ( x ) O As x - 00 , f ( x ) - - what is the end behavior of the function ? - >> -9 ; as x -4 ; as x ∞o , f ( x ) → -9 . - ∞o , f ( x ) → -4 . - 4 ; as x → ∞o , f ( x ) → 4 . - > -​

Answers

Answer:

D

After graphing, you can analyze it accordingly.

An arithmetic sequence is shown in the graph.
What is the equation for the nth term of the arithmetic sequence?

an = –3 + 5(n – 1)
an = –3 + 5(n + 1)
an = –3 – 5n
an = –3 + 5n

Answers

Answer:

an= -3+5(n-1)

Step-by-step explanation:

Try writing out the terms and finding a pattern. In this case, inserting any plotted x-value into the sequence -3+5(n-1) produces the correct y-value.

Answer:

A.) an = -3 + 5(n - 1)

Explanation:

Given: (1, -3), (2, 2), (3, 7), (4, 12), (5, 17)

Arithmetic Series: a + (n - 1)d

['a' is first term, 'n' determines term position, 'd' is common difference]

Determine the following:

a = -3d = second term - first term = 2 - (-3) = 5

Putting into equation:

-3 + (n - 1)5-3 + 5(n - 1)

What are the possible zeros for f(x) equals X to the third power minus 2X to the second power minus 4X +15

Answers

The roots of the polynomial are done by using a calculator will be -2.3671, 2.1835 + 1.2527i, and 2.1835 – 1.2527i.

What are the roots of the polynomial?

The polynomial is given below.

[tex]\rm f(x) = a_0x^n + a_1 x^{n - 1}+ ....+ a_{n-2}x^2 + a_{n-1}x + a_nx^0[/tex]

The roots of the polynomial are equal to n or less than n.

And if one imaginary root is a + bi, then the other imaginary root will be a – bi.

The roots of the polynomial are done by using a calculator.

x = -2.3671, 2.1835 + 1.2527i, 2.1835 – 1.2527i

More about the roots of the polynomial link is given below.

https://brainly.com/question/1514617

#SPJ1

Determine the x and y intercepts of the equation y = -3x + 4.
Select one:
O a. y-int y = 4 and x-int x = 4/3
O b. y-int y = 4/3 and x-int x = 4
O c. y-int y = 4 and No x-int
O d. No y-int and x-int x =4/3​

Answers

Answer:

O c. y-int y = 4 and No x-int

Step-by-step explanation:

In the slope-intercept equation y = -3x + 4, only slope and y-intercept are displayed as it is in slope-intercept format which is y = mx + b; m being the slope and b being the y-intercept.

There is no x-intercept present in a slope-intercept equation.

But due to the 4 being in the place of the y-intercept is the y-intercept of the graph and line depicted off this linear equation (slope-intercept equation).

Hence, the answer is C. Y-intercept = 4 and No x-intercept.

Use interval notation to indicate all real numbers between and including −3 and 5.

Answers

Answer:

[-3,5]

Step-by-step explanation:

Interval notation is a shorthand way of writing and interval of values.  To describe an interval, imagine the two endpoints on the number-line.  Then, list the two endpoint values, leftmost point from the number-line first, separated by a comma.  Lastly, include the appropriate brackets for each endpoint:

Only two brackets total will be used for each interval, a bracket to start it, and one bracket to end it.If a number is included, a square bracket should be used -- either "[" or "]"If the endpoint number is not meant to be included, a 'curved bracket' (which we usually just call a parenthesis) should be used -- either "(" or ")"

For our situation, the two endpoints are -3 and 5.  -3 is to the left of 5 on the number-line, so -3 should be listed first

[tex]-3,5[/tex]

Lastly, the directions say "including -3 and 5", so both endpoints should be included.

To include the -3 on the left, we'll use "["To include the 5 on the right, we'll use "]"

The final result for the interval is [tex][-3,5][/tex]

Other Questions
its math can you help out NEED HELP ASAP !! Which equations are equivalent to 2 + 2 12-x1=1? Check all that apply. The repeating decimal z=0.142857142857142857 as fraction What system did the United States seek to promote throughout the world? WILL GIVE BRAINLEST!!!In the cruise ship hierarchy, a youth staff director would report to thecruise directorchief purserfirst officersecond officer A regular polygon has 18 sides.What is the size of each of its interior angles?Give your answer in degrees (). 13. To strengthen your emotionalintelligence (EQ), you can focus on your self-management. Self-management is the abilitytoA. increase your intelligence quotient (IQ).B. control how others feel or behave.C. change your personality type.D. control your feelings and behaviors. Which expression is equivalent to 2x - x + ?O AOBCD(x - 2)2IN2 X-16 Given 2 (x+3) - 4x = xProve = 2Complete the proof. Provide reasons for 1-6 below. I will give brainiest to the first person who responds BUT only if the answer is correct Which statements describe how traits are inherited? Check all that apply.An offspring always receives different alleles from each parent.An offspring always receives the same alleles from each parent.An offspring can receive different alleles or the same alleles from each parent.Traits are inherited when proteins are passed from parents to offspring.Traits are inherited when genes are passed from parents to offspring.00 4Find the measure of x.X12X = = [?]Round to the nearest hundredth. 1.) Which of the following is the direct speech to the given indirect speech? The employee asked the director whether he could take a few days off to visit his family. a. The employee told, "Could I take a few days off to visit my family?" b. The employee said to the director, "Can I take a few days off to visit my family." c. The employee said to the director, "Can I take a few days off to visit my family?" d. The employee said to the director, "Do I take a few days off to visit my family?" 2.) Which of these is the correct form of reported speech of the given statement? She said to her friend, ''What will you wear for the party tonight?'' a. She told her friend what would she wear for the party tonight. b. She said to her friend what she would wear for the party that night. c. She said to her friend what will she wear for the party in the night. d. She asked her friend what she would wear for the party that night.3.) A/ an _________ begins with a subordinating conjunction. a. independent clauseb. dependent clausec. claused. simple sentenceDo please help me.. I'm stuck in these questions.. HELP ASAP: Which of the following is the best explanation of how jazz helped improve the fortunes of African Americans in the 1920s and 1930s? what organization is a major part of the executive branch? 5. Why did the Soviets build the Berlin Wall? (correct answers only)A sailfish is swimming after a herring in a straight line at 11.8 m/s and begins to accelerate at 6.39 m/s. How long does it take for the sailfish to reach the herring if it is 55.0 m away?(unit=s) According to the "Equal Pay Bill" letter, what will happen it businesses are forced to pay women the same as they pay men? A. Men will make less money. B. The cost of goods and services will increase. C. The government will raise the minimum wage. D. The quality of work will decrease. According to the " Equal Pay Bill " letter , what will happen it businesses are forced to pay women the same as they pay men ? A. Men will make less money . B. The cost of goods and services will increase . C. The government will raise the minimum wage . D. The quality of work will decrease . Match the theories with their characteristics. Precepts about dealing with financial crises that most economists would sign onto are: