Exponential Functions Review

Identify the Variable

100

What does the value of a represent in the exponential function f(x) = ab^x?

y-intercept

200

What does the value of b represent in the exponential function f(x)=ab^x when b is greater than or equal to 1?

growth rate

300

What does the value of b represent in the exponential function f(x)=ab^x when b is less than 1 but greater than 0?

decay rate

400

What does r represent in the exponential growth model f(x) = a(1 + r)^x?

(growth) rate

500

What is (1 - r) called in the exponential decay model f(x) = a(1 - r)^x?

base

Fill in the Blank

100

In the exponential function f(x) = 3(7.25)^x, the y-intercept is __________________. 

3

200

In the exponential function f(x) = 8(2)^x, the growth rate is ______________. 

2

300

The graph of the function f(x) = 2.4(1 - 0.05)^x is __________________ exponentially. 

decaying

400

Consider the function f(x) = 1(4)^x. To increase the y-intercept, you would need a ______________ value than 1.

bigger

500

Consider the function f(x) = 2(1/4)^x. To have a slower decay rate, you would need to divide by a ___________ number than 4. 

smaller

Transformations

100

In the transformed exponential function g(x) = ab^x + k, what does k represent?

a shift

200

In the transformed exponential function g(x) = ab^x + k, what does a represent?

a vertical stretch/compression

300

Consider the parent function f(x) = 1(4)^x. What happens when we transform the exponential function to g(x) = 1(4)^x - 7?

shift down 7 units

400

Consider the parent function f(x) = 1(3.2)^x. What happens when we transform the exponential function to g(x) = 0.5(3.2)^x?

a vertical compression by a factor of 1/2

500

Consider the parent function f(x) = 1(0.75)^x. How would you write its transformed function g(x) to show a shift up of 3 units and a vertical stretch by a factor of 4?

g(x) = 4(0.75)^x + 3

Exponential Models

100

Write an exponential function to model the following situation: There are currently 2 mice in the basement. The population will double every month. 

f(x) = 2(2)^x

200

Write an exponential function to model the following situation: There currently exist 10,000 bacterial cells on the countertop. When you use a cleaner, the population decreases by half every second. 

f(x) = 10000(1/2)^x

300

Write an exponential function to model the following situation: You open an investment account with $4,500. The interest rate is 3%. 

f(x) = 4500(1 + 0.03)^x

400

You buy a car for $30,000. Its value depreciates at a rate of 7% per year. What is its value after 5 years? 

$20,870.65

500

Company A offers a phone at an initial price of $1,200. Its value decreases by 7.2% every year. 

Company B offers a phone at an initial price of $900. Its value decreased by 3.3% every year. 

Which company's phone will be worth more after 4 years?

Company A