QuestionJuly 26, 2025

The initial population of a town is 3600 and it grows with a doubling time of 10 years. What will the population be in 12 years? What will the population be in 12 years? square (Round to the nearest whole number as needed )

The initial population of a town is 3600 and it grows with a doubling time of 10 years. What will the population be in 12 years? What will the population be in 12 years? square (Round to the nearest whole number as needed )
The initial population of a town is 3600 and it grows with a doubling time of 10 years. What will the population be in 12 years?
What will the population be in 12 years?
square 
(Round to the nearest whole number as needed )

Solution
4.1(293 votes)

Answer

8272 Explanation 1. Identify the growth formula Use the exponential growth formula: **P(t) = P_0 \cdot 2^{t/T}**, where P_0 is the initial population, t is time in years, and T is the doubling time. 2. Substitute known values Given P_0 = 3600, t = 12 years, and T = 10 years. Substitute these into the formula: P(12) = 3600 \cdot 2^{12/10}. 3. Calculate the exponent Compute 2^{12/10} = 2^{1.2}. 4. Evaluate the expression Calculate P(12) = 3600 \cdot 2^{1.2} \approx 3600 \cdot 2.2974. 5. Final calculation Multiply to find the population: 3600 \cdot 2.2974 \approx 8271.64.

Explanation

1. Identify the growth formula<br /> Use the exponential growth formula: **$P(t) = P_0 \cdot 2^{t/T}$**, where $P_0$ is the initial population, $t$ is time in years, and $T$ is the doubling time.<br /><br />2. Substitute known values<br /> Given $P_0 = 3600$, $t = 12$ years, and $T = 10$ years. Substitute these into the formula: $P(12) = 3600 \cdot 2^{12/10}$.<br /><br />3. Calculate the exponent<br /> Compute $2^{12/10} = 2^{1.2}$.<br /><br />4. Evaluate the expression<br /> Calculate $P(12) = 3600 \cdot 2^{1.2} \approx 3600 \cdot 2.2974$.<br /><br />5. Final calculation<br /> Multiply to find the population: $3600 \cdot 2.2974 \approx 8271.64$.
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