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If the population of a small town satisfies the exponential model A = 100.01), where is measured in years, how long will it take for the town's population to increasefrom 10,500 to 13,650? Round your answer to two decimal placesAnswerKeypad

If the population of a small town satisfies the exponential model A 10001 where is measured in years how long will it take for the towns population to increasef class=

Respuesta :

We know that the expression for the population is given by:

[tex]A=A_0e^{0.015t}[/tex]

We want to know how long it takes to increase the population from 10500 to 13650. This means that we need to find the time it takes for the population to increase 3150; since this does not depends on the initial population but just in the exponential rate we have:

[tex]\begin{gathered} e^{0.015t}=3150 \\ 0.015t=\ln3150 \\ t=\frac{1}{0.015}\ln3150 \\ t=537.01 \end{gathered}[/tex]

Therefore, it will take 537.01 years to increase the population.

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