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

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: \( \boxed{74688} \)