Exponential Functions

Exponential Growth

100

What is the formula for Exponential Growth?

a(1+r)^x

200

Exponential Growth

P=1000

r=50%

x=3

3375

300

Exponential Growth:

P=3255

r=8%

t=6

5,165.28

400

You deposit $200 into a bank account. Every year that account increases by 12 %. How much will you have after 10 years in your bank account?

621.17

500

The New York Mets sign a new player for $8,000,000 and his salary goes up by 3% every year. How much will he make in his third year?

8,741,816

Exponential Decay

100

What is the formula for Exponential Decay?

a(1-r)^x

200

Exponential Decay:

P=1000

r=50%

x=3

125

300

Exponential Decay:

P=3255

r=8%

t=6

1,973.69

400

The population of an apartment building is 4,000 people. Every month the population goes down by 12%.What is the population after 5 months?

2110.93

500

A certain stock was worth $42 at the beginning of the day. Every hour the stock goes down by 15%. How much will the stock be worth at end of day, 8 hours later?

11.44

Compound Interest

100

What is the formula for compound interest?

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

200

Compounded Monthly:

P=1000

r=50%

t=3

n=12

4,347.46

300

$93 paid at 40% for 10 years compounded Quarterly

4209.11

400

Brenda invests $4,848 in a savings account with a fixed annual interest rate of 5% compounded 2 times per year. What will the account balance be after 6 years?

$6,520.02

500

Lea invests $8,333 in a savings account with a fixed annual interest rate of 8% compounded 2 times per year. What will the account balance be after 12 years?

$21,360.01

Compound Continuously

100

What is the formula for interest compounded continuously?

A=Pe^rt

200

Compounded Continuously:

P=1000

r=50%

t=3

4,481.69

300

***DAILY DOUBLE****

A population of bacteria grows according to the function f(x)=100e^0.02t, where t is measured in minutes. How many bacteria will there be after 4 hours (240 minutes)?

12151.04

400

Jasmine invests $2,658 in a retirement account with a fixed annual interest rate of 9% compounded continuously. What will the account balance be after 15 years?

$10,253.04

500

Maria invests $6,154 in a savings account with a fixed annual interest rate of 8% compounded continuously. What will the account balance be after 10 years?

$13,695.98

Definitions

100

What does r represent?

Rate

200

What does t represent?

Time in years

300

What Does P represent?

Principal

400

What does n represent?

How often interest is compounded

500

What is the formula to find b?

1+-r