Using the Power Property with Exponential Models

to Make Predictions

Section 5.4

Lehmann, Intermediate Algebra, 4edSection 5.4 Slide 2

Using the Power Property with Exponential Models to Make Predictions

Using the Power Property to Make a Prediction

A person invests $7000 in a bank account with a yearly interest rate of 6%, compounded annually. When will the balance be $10,000?

• Let B = f (t) be the balance (in thousand s of dollars) after t years or a fraction thereof•Exponential model of the form f (t) = abt

•B-intercept of (0, 7): $7000, when t = 0,•a = 7 and f (t) = 7bt

Example

Solution

Lehmann, Intermediate Algebra, 4edSection 5.4 Slide 3

Using the Power Property with Exponential Models to Make Predictions

Using the Power Property to Make a Prediction

• End of the year, account increased by 6% of previous years balance• Thus, f (t) = 7(1.06)t• To find when the balance is $10,000 (B = 10),

substitute 10 for f (t) and solve for t

Solution Continued

Lehmann, Intermediate Algebra, 4edSection 5.4 Slide 4

Using the Power Property with Exponential Models to Make Predictions

Using the Power Property to Make a Prediction

Checking solution:

Solution Continued