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When observations begin at $t=0$, a cell culture has $1200$ cells and continues to grow according to the function $p(t)=1200 e^t$, where $p$ is the number of cells and $t$ is measured in days. (a). Compute $p^{\prime}(t)$. What units are associated with the derivative and what does it measure? (b). On the interval $[0,4]$, when is the growth rate $p^{\prime}(t)$ the least? When is it the greatest?

Solution

VerifiedAnswered 1 year ago

Answered 1 year ago

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1 of 2$(a)$ The derivation of the function for a number of units represents the rate of growth of the colony.

$\begin{align*} p'(t)&=\left(1200e^t\right)'\\ &=1200e^t\ \text{cells/day} \end{align*}$

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