Warm Up

In the textbook…

p. 436 #1 – 3

Read directions about x values!

Questions?

Exponential Growth

Objective: To learn to model exponential growth.

exponential growth – is an exponential function where a > 0 and b > 1.

Starting Amount

(when x = 0)

Growth Factor

Growth Factor

b = 100% + rate of growth

Writing an Equation for Exponential Growth

1. A new automobile currently cost $17,000. The cost increase 5% per year.

Writing an Equation for Exponential Growth

2. The cost of tuition at a college is $12,000 and is increasing at a rate of 6% per year.

Writing an Equation for Exponential Growth

3. The population of a city of 450,000 people increases 2.5% per year.

Writing an Equation for Exponential Growth

4. The number of student-athletes at West Johnston High School is 300 and is increasing at a rate of 8% per year.

Practice!

In the Practice Workbook…

Reteaching 8-8 (p. 109)

# 1 – 3

Assignment

In the textbook…

p. 441-442

# 1 – 10, 31, 35

Warm Up

In the Practice Workbook…

Practice 8-8 (p. 110)

#1, 3, 5

Questions?

Compound Interest

Objective: To learn use exponential growth to calculate compound interest.

simple interest – interest paid only on the principal.

I = p ∙ r ∙ t

Principal (amount invested)

Interest Rate (as a decimal)

Time (in years)

InterestedEarned

Compound Interest

interest paid on both principal and the interest that has already been earned

Example 1

You invest $5000 in an account paying 6% compounded annually. Find the account balance after each of the following years.

a) 1 yr b) 5 yr c) 10 yr d) 20 yr

Example 2

You invest $2500 in an account paying 7.25% compounded annually. Find the account balance after each of the following years.

a) 1 yr b) 2 yr c) 6 yr d) 25 yr

Example 3

You invest $28,000 in an account paying 4% compounded annually. Find the account balance after each of the following years.

a) 1 yr b) 2 yr c) 5 yr d) 15 yr

Compound Interest

Over the year you have options on how many times during the year the amount is calculated!

Compounded Periods Per Year

annually 1

semi-annually 2

quarterly 4

monthly 12

daily 365

Example 4 “semi-annually”

You invest $5000 in an account paying 6% per year (APR). Find the account balance after 15 years with the interest compounded semi-annually.

Example 5 “quarterly”

You invest $5000 in an account paying 6% per year (APR). Find the account balance after 15 years with the interest compounded quarterly.

Example 6 “monthly”

You invest $5000 in an account paying 6% per year (APR). Find the account balance after 15 years with the interest compounded monthly.

Example 7 “daily”

You invest $5000 in an account paying 6% per year (APR). Find the account balance after 15 years with the interest compounded daily.

Formula for Compound Interest

A = P ∙

Principal (amount invested)

Total AmountEarned

Number of periods per year

Time (in years)

Interest Rate (as a decimal)

Assignment

Calculating

Compound Interest

Worksheet