Chapter 2.7, Problem 12E

To determine

To Sketch: The graph of $P^{\prime }$ and illustrate about the yeast population.

Explanation of Solution

Given that, the graph represents the population function $P\left(t\right)$ for yeast cells in a laboratory culture.

From the graph, it is very clear that the slope of the graph is always positive. This implies that the derivative of the graph must have a positive functional value.

Initially, the value of $P\left(t\right)$ is very small and its starts increasing rapidly before $t=5$ hours and then the increase becomes negligible just after $t=10$ and becomes constant

after a very long time.

This implies that the graph of $P^{\prime }\left(t\right)$ initially starts with a very low value and it keep increasing rapidly and then reaches the maximum value between $t=5$ and $t=10$.

Then, the value of $P^{\prime }\left(t\right)$ decreases and gets closer to zero.

Graph:

Use the above information and trace the graph of $P^{\prime }\left(t\right)$ as shown below in Figure 1.

Illustration:

The graph indicates about the rapid growth of yeast in between $t=5$ and $t=10$ and then the growth rate declines afterwards.