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Calculus / Precalculus With Limits A Graphing Approach 5 / Chapter 3.5 / Problem 3.5.28

Precalculus With Limits A Graphing Approach | 5th Edition | ISBN: 9780618851522 | Authors: Ron Larson Robert Hostetler, Bruce H. Edwards, David C. Falvo (Contributor)

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Population The populations P (in thousands) of Pittsburgh,

Chapter 3, Problem 3.5.28

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QUESTION:

Population The populations P (in thousands) of Pittsburgh, Pennsylvania from 1990 to 2004 can be modeled by \(P=372.55 e^{-0.01052 t}\), where t is the year, with \(t=0\) corresponding to 1990. (Source: U.S. Census Bureau)

(a) According to the model, was the population of Pittsburgh increasing or decreasing from 1990 to 2004? Explain your reasoning.

(b) What were the populations of Pittsburgh in 1990, 2000, and 2004?

(c) According to the model, when will the population be approximately 300,000?

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QUESTION:

Population The populations P (in thousands) of Pittsburgh, Pennsylvania from 1990 to 2004 can be modeled by \(P=372.55 e^{-0.01052 t}\), where t is the year, with \(t=0\) corresponding to 1990. (Source: U.S. Census Bureau)

(a) According to the model, was the population of Pittsburgh increasing or decreasing from 1990 to 2004? Explain your reasoning.

(b) What were the populations of Pittsburgh in 1990, 2000, and 2004?

(c) According to the model, when will the population be approximately 300,000?

ANSWER:

Step 1 of 6

(a)

Let us find the model for the population of the country in the year 1990.

Substitute 0 for t in \(P=372.55 e^{-0.01052 t}\) and simplify.

\(\begin{aligned}
P & =372.55 e^{-0.01052 t} \\
P & =372.55 e^{-0.01052(0)} \\
& =372.55(1) \\
& =372.55
\end{aligned}\)

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