Mathematics Middle School

Consider the standard form of an exponential function:

[tex]y=a(b)^x[/tex]
How does changing the base number (inside the parentheses) change your graph?

Answers

Answer 1

Answer:

Step-by-step explanation:

Challenge 1

We have exponential decline if 0 b 1. As you move from left to right, the curve will get less steep.

If b is greater than 1, exponential growth is present, and the curve slopes upward from left to right.

Examples include exponential decline (y = 2(0.5)x) and exponential growth (y = 2(1.2)x).

Remember that b cannot be negative.

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Challenge 2

In the general template provided, enter x = 0.

y = a(b)^x

y = a(b)^0

y = a(1) (1)

y = a

When x = 0 is plugged in, the result is y = a.

The curve is therefore on the point (0,a). The y intercept appears here. It is the point when the curve veers off the y axis. The y intercept is altered if the value of "a" is altered.

Examples:

Related Questions

Cubes needed to fill Prism 6:_____cubes
Volume of Prism 6: _______cubic units. (sorry if the pic is messy.) HELP ME I need to FINISH TONIGHT I'm GIVING OUT 30 POINTS!!!!!!

Answers

Answer:

125 cubic units

Step-by-step explanation:

the volume formula is length x width x height.

because the length, width, and height of the prism are all 5 units, the volume of the prism is 125 cubic units.

hope this helped, good luck!

125 cubic units it’s okay ur pix isn’t that messy lol

Can you solve this for me? Thank you! :>

Answers

Whatever you do to one side you do to the other
it'll be the last one, whatever you do on one side of the equation, you do to the other side.

Determine whether the survey question may be biased.
Do you think that the city council should approve the construction of a skate park in our town?

Answers

Answer: Yes they should and no it's not biased

Step-by-step explanation: I don't know my opinion is that it isn't bias

consider the expression 4(8x+5)
complete 2 descriptions of parts the expression
1. the entire expression is the product of ____.
2. on its own, (8x+5) is a sum with ___.

the choices are
2 factors
3 factors
2 terms
3 terms

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..

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.....

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Answer: 2 factors 2 terms

Step-by-step explanation:

Can you give me the answer to this? Thank you!

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Answer:Multiply or divide in order left to right

Step-by-step explanation:

Left to right multiplication to divide sk anger 1(a)

Can you solve this for me? Thank you! :>

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Answer:

B

Step-by-step explanation:

< just means more of and since it says more than 250 the answer would have to be something grater than 250

Hope this helps!

C. The number of people who attended the funeral was fewer than 250

X or the number of people < (less than) 250

please help i need this very soon

Answers

Answer:

for a it is $20

for b it is $10

question A is $20
question B is $10

HELP HELP HELP HELP
I need math

DUE today

Answers

Answer:

1.<3592

2.<623

3. <942

4. <829

5.692

6.986

Step-by-step explanation:

Which equations shows the variable terms isolated on one side and the constant terms isolated on the other side for the equation 3x - 5 = -2x + 10? Select two options.
A. x = 5
B. –15 = –5x
C. 5x = 15
D. –15 = 5x
E. x = -5

Answers

Answer:

A. No Solutions

B. X=3

C. X=3

D. No Solutions

E. No S

Can you solve this for me? Thank you! :>

Answers

Answer:

Whatever you do one one side of the equal sign, you must do on the other side.

Step-by-step explanation:

It’s D “Whatever you do to one side of the equal sign, you must copy and do on the other side of the equal side.

So I kinda need some more help that would be appreciated

Answers

Answer:

75 percent of a positive number is greater greater than 50 percent of a positive number. and the second one is 75percent of a negative number is less than 50percent of a negative number

Answer:

Step-by-step explanation:

75% of 100> 50% of 100

75% of 1< 50% of 100

Find the algebraic expression:
36a+28

Answers

Answer:

Step-by-step explanation:

4(9a+7)

Please Mark me brainiest

Match the terms to their definition. 1 . a number that is less than zero positive number 2 . a number belonging to the set made up of the counting numbers: 1, 2, 3, and so on integer 3 . a number that is greater than zero negative number 4 . a number belonging to the set made up of the whole numbers and their opposites opposite numbers 5 . a line that graphically represents all numbers natural number 6 . two numbers that are the same distance from zero on the number line, but in opposite directions number line

Answers

Answer: 1. Negative number

2. Natural number

3. Positive number

4. Integers

5. Number line

6. Opposite numbers

Step-by-step explanation:

1. The first statement says a number that is less than zero, which means any negative number would be less than zero. For example (-1), (-2), etc.

2. The second statement is asking for numbers belonging to the counting set, which means starting from one (1). Natural numbers are numbers that start from 1 and don't include negative numbers or zeros.

3. The third statement says the number that is greater than zero, as negative numbers are smaller than zero and the natural number option has already been chosen above, we will consider positive numbers.

4. Whole numbers consist of both negative and positive integers including zero. Therefore, a set of whole numbers will be written as integers.

5. Number line is a line that represents both negative and positive numbers.

6. Consider an example- (+5) and (-5), both the numbers are the same but with different signs, making them opposite of each other. Therefore, the correct answer would be opposite numbers.

How do I simplify Rational Exponents and Radicals?
I was absent yesterday and we completely moved onto a brand new subject. I don't quite understand, this isn't asking me to solve it, It's asking me to simplify it. help??

Some of the problems I don't understand:
4x⁻⁴y⁴
-2x⁴y⁻¹

Answers

Rational exponents and radicals are simplified in a similar way to how other exponents and radicals are simplified.

For the first expression 4x⁻⁴y⁴, you can simplify it by noticing that it has a negative exponent on the x term and a positive exponent on the y term. To simplify, you can keep the base (x and y) and the exponent (4 and -4) but you change the negative exponent to a fraction and change the sign:

4x⁻⁴y⁴ = (x^-4) (y^4) = x^-4y^4

For the second expression -2x⁴y⁻¹, you can simplify it by noticing that it has a negative exponent on the y term. To simplify, you can keep the base (x and y) and the exponent (4 and -1) but you change the negative exponent to a fraction and change the sign:

-2x⁴y⁻¹ = -2 (x^4) (y^-1) = -2x^4y^-1

To simplify these expressions further, you would need to know the specific values of x and y. But these are the steps to simplify a rational exponent or radical to its simplest form.

It's also worth mentioning that if you have a fractional exponent you can simplify it by raising the base to the numerator of the exponent and the denominator of the exponent. For example, x^(3/4) = (x^3)^(1/4) = ∛x

Keep in mind that when you simplify rational exponents or radicals, you should always keep the base and the exponent, and only change the sign of the exponent if it is negative.

A hot air balloon was at a height of 60 feet above the ground when it began to ascend. The balloon climbed at a rate of 15 feet per minute. Let t represent the time in minutes since the balloon began climbing. Write an algebraic equation for a sequence that can be used to find the height, h, of the balloon after t minutes.
a. Make a table that shows the heights of the hot air balloon after climbing for 1,2,3, and 4 minutes


B. Let t represent the time in minutes since the ballon began climbing. Write and algebraic equation for a sequence that can be used to find the height, h, of the balloon after t minutes

C. Use your equation from part b to find the height, in feet, of the hot air balloon after climbing for 8 minutes



PLEASE HELP!!!!!!!!! I NEED THIS QUESTION. Would be greatly appreciated for the answer. Thank you

Answers

Wow soo many points 50 I think the answer will be 15 minutes so the answer will be 60

Can someone pls help?!

Find the product of........ The rest of the question is down below.

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Answer: The answer is −2x+14 just take away the parentheses.

Please answer it brainless

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Answer:

[tex]y=\frac{1}{2}x+1[/tex]

Step-by-step explanation:

We have the one tablet taken to start so that is where the +1 comes from.

We also have the 1/2 tablet taken each month after that so it is 1/2 times the number of months x.

y= 1/2x + 1>>>>>>>>>>

What is the surface area of this right rectangular prism with dimensions of 4 centimeters by 4 centimeters by 6 centimeters?

Answers

C 128 tell me if I’m wrong

Answer:

128

Step-by-step explanation:

A=2(wl+hl+hw)=2·(4·4+6·4+6·4)= 128

40 points to whoever answers this right :)

Answers

Answer:

the answer to your question is -2

-2 is the right answer

I Will give brainliest to the first one that answer
Need help ASAP

Answers

Answer:

B. 80 + 45 + 5x = 180

Step-by-step explanation:

In this problem, we are asked to construct an equation that can be used to solve for x.

The measures of the interior angles of a triangle add to 180º. Therefore, we can construct the following equation:

A + B + C = 180º

In this problem, we are given all of the shown triangle's angles: A = 80º, B = 45º, and C = 5xº. Thus, we can plug those values in for A, B, and C in the above equation.

80º + 45º + 5xº = 180º

This happens to be option B.

Answer: 80+45+5x=180

Step-by-step explanation: Angles in a triangle sum up to 180 degrees.

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