Question

the population of a slowly growing bacterial colony after t hours is given by p(t)=5t^{2}+35t + 200. find the growth rate after 2 hours.

Explanation:

Step1: Find the derivative of $p(t)$

The derivative of $p(t)=5t^{2}+35t + 200$ using the power - rule $\frac{d}{dt}(at^{n})=nat^{n - 1}$ is $p^\prime(t)=10t+35$.

Step2: Evaluate $p^\prime(t)$ at $t = 2$

Substitute $t = 2$ into $p^\prime(t)$. So $p^\prime(2)=10\times2+35$.
$p^\prime(2)=20 + 35=55$.

Answer:

55