Question

1. suppose that the future population of a town t years after january 1, 1995, is described in thousands by the function p(t)=120 + 4t+0.05t². calculate the value of p(10) and explain its meaning.

Explanation:

Step1: Substitute t = 10 into the function

Substitute \(t = 10\) into \(P(t)=120 + 4t+0.05t^{2}\).

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Step2: Calculate each term

First, calculate \(4\times10 = 40\) and \(0.05\times10^{2}=0.05\times100 = 5\).

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Step3: Sum up the terms

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The function \(P(t)\) gives the population of the town in thousands \(t\) years after January 1, 1995. When \(t = 10\), it means 10 years after January 1, 1995 (i.e., January 1, 2005), the population of the town is 165,000.

Answer:

\(P(10)=165\), which means the population of the town in thousands on January 1, 2005 is 165, so the actual population is 165,000.