Solve a multi-step problem EXAMPLE 5 Forestry The number of acres of Ponderosa pine forests decreased in the western United States from 1963 to 2002 by.

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Solve a multi-step problem EXAMPLE 5 Forestry The number of acres of Ponderosa pine forests decreased in the western United States from 1963 to 2002 by 0.5% annually. In 1963 there were about 41 million acres of Ponderosa pine forests. a. Write a function that models the number of acres of Ponderosa pine forests in the western United States over time.

Solve a multi-step problem EXAMPLE 5 SOLUTION P = a(1 – r) t Write exponential decay model. = 41(1 –0.005) t Substitute 41 for a and for r. = 41(0.995) t Simplify. a.a. Let P be the number of acres (in millions), and let t be the time (in years) since The initial value is 41, and the decay rate is b. To the nearest tenth, about how many million acres of Ponderosa pine forests were there in 2002?

Solve a multi-step problem EXAMPLE 5 P = 41(0.995) Substitute 39 for t. Use a calculator. ANSWER There were about 33.7 million acres of Ponderosa pine forests in b. To the nearest tenth, about how many million acres of Ponderosa pine forests were therein 2002 ?

GUIDED PRACTICE for Example 5 WHAT IF? In Example 5, suppose the decay rate of the forests remains the same beyond About how many acres will be left in 2010? 5. SOLUTION P = a(1 – r) t Write exponential decay model. = 41(1 –0.005) t Substitute 41 for a and for r. = 41(0.995) t Simplify. a.a. Let P be the number of acres (in millions), and let t be the time (in years) since The initial value is 41, and the decay rate is

GUIDED PRACTICE for Example 5 To find the number of acres will be left in 2010, 47 years after 1968, substitute 47 for t P = 41(0.995) 47 Substitute 47 for t. = 32.4 There will be about 32.4 million acres of Ponderosa pine forest in ANSWER