Module D: Exponential Functions

Question 1

A^m * A^n

What is the result and what is the name of this property?

Answer 1

A^(m+n)

This is the product property of exponents

Question 2

3x^-2y^6 / 18x^-1y^3

Answer 2

y^3 / 6x

Question 3

a^2 * a^3 =

Answer 3

a^5

Question 4

3x^3 * 5x^-2

Answer 4

15x

Question 5

8x^7 / 2x^3

Answer 5

4x^4

Question 6

5x^-2

Answer 6

5 / x^2

Question 7

A^m / A^n

What is the result and what is the name of this property?

Answer 7

A^(m-n)

This is the Quotient Property of Exponents

Question 8

( A^m )^n

What is the result and what is the name of this property of exponents?

Answer 8

A^(mn)

This is the Power Property of Exponents

Question 9

What is the format for the EQUATION of an exponential function?

Answer 9

f(x) = a(b)^x

Question 10

f(x) = a(b)^x

What does each part of the equation represent?

Answer 10

a = y-intercept
b = factor

Question 11

f(x) = 3(2)^x

Describe this exponential TABLE

Answer 11

It will have a y-intercept of 3 and the outputs will DOUBLE in value for each consecutive row

Question 12

f(x) = 10(0.88)^x

Describe the CONTEXT of this equation. Assume it is measuring money in days.

Answer 12

• Start with 10 dollars

* Lose 12% of amount each consecutive day.

Question 13

f(x) = 10000(1.05)^x

Describe the CONTEXT of this exponential function

Answer 13

• Starts at 10k

* Grows by 5% each time

Question 14

f(x) = a(b)^x

Describe the importance of the value of “b” in terms of EGTC

Answer 14

• When evaluating into the EQUATION, b is first raised to the x power. Then you can multiply the a value.
• On a GRAPH, b will determine if the function grows or decays. If b>1, increase. If 0

Question 15

If f(x) = 5(2)^x, how do you find the result for f(3)?

Answer 15

f(3) = 5(2)^3
f(3) = 5(8)
f(3) = 40

Question 16

For g(x) = 40(3)^x, John is trying to find g(2).
John thinks that the answer is 14400.
Is he right? Explain?

Answer 16

He is WRONG. g(2) = 40(3)^2, which means g(2) = 40(9) = 360.

Perhaps John incorrectly thought 120^2.

Question 17

If you want to find the future value of a 100000 house, which grows in value exponentially by 5%, after 10 years, what would be a DIRECT way of finding the answer?

Answer 17

100000(1.05)^10

= 162889