The growth rate of the population of a county is
\[
P^{\prime}(t)=\sqrt{t}(3370 t+7050)
\]
where $t$ is time in years. How much does the population increase from $t=1$ year to $t=4$ years?
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Answer

Final Answer: $ \boxed{74688} $

Steps

Step 1 ：To find the increase in population from $ t=1 $ year to $ t=4 $ years, we need to integrate the given growth rate function $ P'(t) $ over the interval from $ t=1 $ to $ t=4 $.

Step 2 ：Let $ P'(t) = \sqrt{t}(3370t + 7050) $.

Step 3 ：Integrate $ P'(t) $ from $ t=1 $ to $ t=4 $ to find the population increase.

Step 4 ：The population increase is $ 74688 $.

Step 5 ：Final Answer: $ \boxed{74688} $

The growth rate of the population of a county is\[P^{\prime}(t)=\sqrt{t}(3370 t+7050)\]where $t$ is time in years. How much does the population increase from $t=1$ year to $t=4$ years?Sontint druerTres opgs

Answer

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The growth rate of the population of a county is
\[
P^{\prime}(t)=\sqrt{t}(3370 t+7050)
\]
where $t$ is time in years. How much does the population increase from $t=1$ year to $t=4$ years?
Sontint druer
Tres opgs