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Modeling Number of Acres of Ponderosa Pine Forests in the Western United States

This function calculates the number of acres of Ponderosa pine forests in the western United States over time using an exponential decay model.

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Modeling Number of Acres of Ponderosa Pine Forests in the Western United States

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  1. a. Write a function that models the number of acres of Ponderosa pine forests in the western United States over time. EXAMPLE 5 Solve a multi-step problem 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.

  2. To the nearest tenth, about how many million acres of Ponderosa pine forests were there in 2002? a. LetPbe the number of acres (in millions), and lett be the time (in years) since 1963. The initial value is 41, and the decay rate is 0.005. EXAMPLE 5 Solve a multi-step problem SOLUTION P = a(1 –r)t Write exponential decay model. = 41(1 – 0.005)t Substitute 41 for a and 0.005 for r. = 41(0.995)t Simplify.

  3. To the nearest tenth, about how many million acres of Ponderosa pine forests were there in 2002? P = 41(0.995)3933.7 ANSWER There were about 33.7 million acres of Ponderosa pine forests in 2002. EXAMPLE 5 Solve a multi-step problem Substitute 39 for t. Use a calculator.

  4. WHAT IF?In Example 5, suppose the decay rate of the forests remains the same beyond 2002. About how many acres will be left in 2010? 5. ANSWER There will be about 32.4 million acres of Ponderosa pine forest in 2010. for Example 5 GUIDED PRACTICE

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