#### To determine

**To Sketch:** The graph of P′ and illustrate about the yeast population.

#### Explanation

Given that, the graph represents the population function P(t) 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(t) 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′(t) 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′(t) decreases and gets closer to zero.

**Graph:**

Use the above information and trace the graph of P′(t) 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.