EXPONENTIAL FUNCTIONSApplication Problems

(or in other words…..Word Problems!)

Exponential Functions

Population Growth How does our population grow? Does each person just have one child or

is there some other rate of growth out there?

Population growth is not linear. If it was, there would not be controls on reproduction is some countries!

The formula for population growth is exponential!

Exponential Functions

Population Growth is given by the formula:

P = Population at time t = Population at t = 0 D = doubling time

Exponential Functions

Population Growth In 2004, the population in Kazakhstan reached

15 million. It is estimated that the population will double in 30 years. If the population continues to grow at the same rate, what will the population be 20 years from now?

= 15(2)20/30

= 23.81 So in 20 years, there will be approximately

23.81 million people in Kazakhstan.

d = 30t = 20

Exponential Functions

Population Growth

What will the approximate population in Kazakhstan be in 40 years?

37.80 million!!!

Exponential Growth

Compound Interest Compound interest is different from

simple interest because this is the idea that a person is paying interest on interest.

What???? When you use your credit card, you pay

interest. If it is not paid off, then the next statement will show interest on the interest and the original charge.

That is why credit cards can be so bad!!

Exponential Functions

Compound Interest

A = the amount at the end P = amount initially invested (principal) r = interest rate as a decimal n = number of times compounded per year t = time in years

Exponential Functions

Compound Interest If $3,000 is deposited in an account

paying 3% compounding quarterly, how much will you have in the account in 7 years?

= 3000(1 + )4*7

= 3000(1 + )28

= $3,698.14

P = 3000r = 0.03 (change % to a decimal)

n = 4 t = 7

Exponential Functions

If $5,000 is deposited in an account paying 6% compounded annually, how much will you have in the account in 4 years?

$6,312.38

Exponential Functions

Be careful when entering in the exponents.

Make sure your answers make sense. Remember to change percents to

decimals. It may be helpful to identify each variable

before beginning the problems!