If the population growth ($P$) in a community is projected to follow the function $P= 7t^2 + 5t + 350$ ($t$ is time in years), then find the instantaneous rate of growth from the second year to third year.
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$\begingroup$$P'(t)=14t+5$
$P'(2)=33$
Therefore $33$ is your answer.
To get this answer I took the derivative of your function and got the rate at which $P$ changes with respect to $t$
$\endgroup$ 3 $\begingroup$Well, this question is not at all clear. It asks for the "instantaneous rate of growth from the second to third year", as if there is a single number for the answer. But "from the second to third year" the "instantaneous rate of growth" is continually changing, per the formula 14*t + 5, as t increases continuously from 2 to 3.
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