EXAMPLE 4 Solve a multi-step problem The owner of a 1953 Hudson Hornet convertible sold the car at an auction. The owner bought it in 1984 when its value.

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EXAMPLE 4 Solve a multi-step problem The owner of a 1953 Hudson Hornet convertible sold the car at an auction. The owner bought it in 1984 when its value was $11,000. The value of the car increased at a rate of 6.9% per year. COLLECTOR CAR

EXAMPLE 4 SOLUTION a.a. Write a function that models the value of the car over time. b.b. The auction took place in What was the approximate value of the car at the time of the auction ? Round your answer to the nearest dollar. a.a. Let C be the value of the car (in dollars), and let t be the time (in years) since The initial value a is $11,000, and the growth rate r is Solve a multi-step problem

EXAMPLE 4 C = a(1 + r) t Write exponential growth model. Substitute 11,000 for a and for r. = 11,000( ) t Simplify. = 11,000(1.069) t b.b. To find the value of the car in 2004, 20 years after 1984, substitute 20 for t. Substitute 20 for t. C = 11,000(1.069) 20 Use a calculator. ≈ 41,778 Solve a multi-step problem

EXAMPLE 4 ANSWER In 2004 the value of the car was about $41,778. Solve a multi-step problem

Standardized Test Practice EXAMPLE 5 You put $250 in a savings account that earns 4% annual interest compounded yearly. You do not make any deposits or withdrawals. How much will your investment be worth in 5 years ? $300 A $ B $781,250 D $ C y = a(1 + r) t = 250( ) 5 = 250(1.04) 5 ≈ Write exponential growth model. Substitute 250 for a, 0.04 for r, and 5 for t. Simplify. Use a calculator. You will have $ in 5 years. SOLUTION

Standardized Test Practice EXAMPLE 5 ANSWER A D CB The correct answer is B.

GUIDED PRACTICE for Examples 4 and 5 5. WHAT IF? In example 4, suppose the owner of the car sold it in Find the value of the car to the nearest dollar. ANSWER In 2004 the value of the car was about $21, WHAT IF? In example 5, suppose the annual interest rate is 3.5%. How much will your investment be worth in 5 years? ANSWERYou will have $ in 5 years.