Using the Power Property with Exponential Models to Make Predictions Section 5.4 Using the Power Property with Exponential Models to Make Predictions

Using the Power Property with Exponential Models to Make Predictions Using the Power Property to Make a Prediction Example 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 Solution Section 5.4 Slide 2

Using the Power Property with Exponential Models to Make Predictions Using the Power Property to Make a Prediction Solution Continued 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 Section 5.4 Slide 3

Solution Continued Checking solution: Using the Power Property with Exponential Models to Make Predictions Using the Power Property to Make a Prediction Solution Continued Checking solution: Section 5.4 Slide 4