Question

the population of a slowly growing bacterial colony after t hours is given by p(t)=3t^{2}+28t + 100. find the growth rate after 4 hours.

Explanation:

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

The derivative of $p(t)=3t^{2}+28t + 100$ using the power - rule $\frac{d}{dt}(at^{n})=nat^{n - 1}$ is $p^\prime(t)=\frac{d}{dt}(3t^{2})+\frac{d}{dt}(28t)+\frac{d}{dt}(100)$.
$p^\prime(t)=6t + 28$.

Step2: Evaluate $p^\prime(t)$ at $t = 4$

Substitute $t = 4$ into $p^\prime(t)$.
$p^\prime(4)=6\times4+28$.
$p^\prime(4)=24 + 28=52$.

Answer:

52