8.5 Writing Exponential Writing Exponential Growth FunctionsGrowth Functions

Objective I will use the equation for exponential growth to find resulting balances.

Key Words •exponential function•growth factor•growth rate

Exponential Growth

8.5 Exponential Growth Functions

C is initial amountr is the growth rate t is the time period

Exponential Growth - growth in which a quantity increases by the same percent in each unit of time

Growth Factor - (1 + r); how much growth there is total; original amount plus percent increase

Growth Rate - r; how much growth there is in addition to the original amount; percent increase

y C(1 r)t

8.5 Exponential Growth Functions

Use the exponential growth model to find the account balance.1. A principal of $450 is deposited in an account that pays 2.5% interest compounded yearly. Find the account balance after 2 years.

y1 450(1.025) 461.25

y2 450(1.025)(1.025) 472.78

Method 1: Solve a simpler problem

Original balance increases 2.5% per year, so growth factor is 102.5% or 1.025

Year 1

Year 2

The account balance will be about $472.78 after two years.

8.5 Exponential Growth Functions

Use the exponential growth model to find the account balance.1. A principal of $450 is deposited in an account that pays 2.5% interest compounded yearly. Find the account balance after 2 years.

y C(1 r)t

y 450(1 0.025)2

y 450(1.025)2

y 450(1.051)

y 472.95

Method 2: Use the formula

Equation

Substitute

Add

Exponent

MultiplyThe account balance will be about $472.95 after two years.

Exponential Growth

8.5 Exponential Growth Functions

Guided Practice: Use the exponential growth model to find the account balance.

C is initial amountr is the growth rate t is the time period

2. A principal of $800 is deposited in an account that pays 3% interest compounded yearly. Find the account balance after 5 years.

5

y C(1 r)t

Guided Practice: Finding an Initial Investment

3. How much must you deposit in an account that pays 4% interest compounded yearly to have a balance of $2000 after 5 years?

Exponential Growth

y C(1 r)t

Writing an Exponential Growth Model

4. A population of 50 pheasants is released in a wildlife reserve. The population triples each year for 3 years. What is the population after 3 years?

y C(1 r)t

y 50(1 2)3

y 50(3)3

y 50(27)

y 1350

Population Triples - Growth Factor = 3Growth Factor = 1 + r3 = 1 + rr = 2

There will be 1350 pheasants after 3 years.

Graphing an Exponential Growth Function

• Graph like any other exponential function– Make a table of values– Input x-values into the exponential growth

function equation - y = C(1 + r)t

– How many values? 5

5. Graph the exponential growth model in Exercise 3.

1 2 3 4 5

5000

4000

3000

2000

1000

x y

y C(1 r)t

y 50(3)t

0

1

2

3

4

50

150

450

1350

4050

50(3)0

50(1)

50(3)1

50(3)

50(3)2

50(9)

50(3)3

50(27)

50(3)4

50(81)

Guided PracticeRichard opens a bank account with $1000 that pays a 4% interest rate. Write an exponential growth function to find the amount of money in the account after t years. Then graph the function.

y C(1 r)t x y

y 1000(1.04)t

Independent Practice

A pack of wolves starts with 8 wolves. The number of wolves in the pack doubles each year. Write an exponential growth function to represent the situation. Then graph the function to find how many wolves will be in the pack after 4 years.