Exponential Functions Review

Interpret the Function

100

Is this function growth or decay?

y=155(0.23)^x

Exponential decay

200

What is the initial amount?

y=1234(1.15)^x

1,234

300

What is the percentage of increase/decrease?

y=275(1.017)^x

1.7%

400

What is the percentage of increase/decrease?

y=1500(0.83)^x

17%

500

Why is base e used in this function?

y=2035e^0.07t

This function represents continuous growth

Word Problems

100

There are currently 250 polar bears in the wild. Their population is decreasing by 23% each year. How many polar bears will remain in 10 years. 

Approximately 18 polar bears

200

If you deposit $150 into a savings account that pays 3% annual interest, how much will you have in the account after 7 years?

$184.48

300

In 2001, you invested $575 into an account that pays 4.7% annual interest. What will the value by in 2015?

$1,093.76

400

You bought a brand new Jeep for $35,000. Each year its value depreciates 6.7% What will it be worth in 8 years?

$20,096.54

500

You borrowed $25,000 from the bank to remodel your kitchen. If they charge 13.5% interest annually, how much will you owe in 2 years?

$32,205.63

Describe the Transformation

100

Describe the transformation on  y=4^x:

y=(4^x)-12

Shifted down 12 units

200

Describe the transformation on y=5^x:

y=45(5)^x

Vertically stretched by a factor of 45

300

Describe the transformation:

y=(1/2)^x + 3

Reflected over the y-axis and shifted up 3 units

400

Describe the transformation on y=3^x:

y= -3^(x+5)

Reflection over the x-axis and shifted left 5 units

500

Describe the transformation on y=2^x:

y= -2^-x

Reflected over the x-axis and reflected over the y-axis

Create the Function

100

Write an equation: A diamond valued at $4500 appreciated in value by 4.2% each year.

y=4500(1.042)^x

200

Write the equation: An exponential function with a base of 4 that has been compressed by a factor of 1/2 and shifted right 3 units. 

y= (1/2)4^x-3

300

Write the equation: An endangered species that currently has 300 in the wild and declines by 27% each year.

y=300(0.73)^x

400

Write the equation: An investor deposits $1,000 into an account that promises an annual interest rate of 5% compounded semi-annually.

A(t)=1000(1.025)^2t

500

Write the equation: The population of Austin, Texas in 2010 was 790,000. The population continues to grow continuously at a rate of 3.9% each year.  

N(t)=790,000e^0.039t

Compound Interest

100

What is the compound interest formula?

A(t)=P(1+r/n)^nt

200

How often is interest being compounded in this formula?

A=300(1+0.063/52)⁵²⁽¹⁰⁾

Weekly

300

You currently owe $400 on your visa credit card. They charge 14% annual interest compounded monthly. If you stop making payments, how much will you owe in 5 years?

$802.24

400

Your bank pays 3% interest compounded quarterly. If your first deposit is $700, how much will you owe in 4 years? 

$788.89

500

If you invest $2,000 at an annual interest rate of 13% compounded continuously, calculate the final amount you will have in the account after 20 years.

$26,927.48