Chapter 2 - Section 2.8 - The Derivative as a Function - 2.8 Exercises - Page 162: 13

(a) $C'(t)$ is the rate of change of the percentage of full charge with respect to time. (b) We can see a graph of $C'(t)$ below. The graph shows that initially, the percentage of full charge increases quickly. As time passes, the increase per unit time gets closer to zero as time $t$ gets closer and closer to 12 hours.

(a) $C'(t)$ is the rate of change of the percentage of full charge with respect to time. $C'(t)$ tells us how quickly the percentage of full charge is increasing at time $t$ (b) We can see a graph of $C'(t)$ below. The graph shows that initially, the percentage of full charge increases quickly. As time passes, the percentage of full charge increases more slowly and the increase per unit time gets closer to zero as the battery gets closer and closer to the fully charged level.