?A rechargeable battery is plugged into a charger. The graph shows C(t), the percentage

Chapter 2, Problem 13

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QUESTION:

A rechargeable battery is plugged into a charger. The graph shows C(t), the percentage of full capacity that the battery reaches as a function of time t elapsed (in hours).

(a) What is the meaning of the derivative \(C^{\prime}(t)\)?

(b) Sketch the graph of \(C^{\prime}(t)\). What does the graph tell you?

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QUESTION:

A rechargeable battery is plugged into a charger. The graph shows C(t), the percentage of full capacity that the battery reaches as a function of time t elapsed (in hours).

(a) What is the meaning of the derivative \(C^{\prime}(t)\)?

(b) Sketch the graph of \(C^{\prime}(t)\). What does the graph tell you?

ANSWER:

Step 1 of 3

The meaning of derivative of \(C^{\prime}(t)\) is the ratio of change of percentage of full capacity in a very infinitesimal change of time.

\(C^{\prime}(t)=\lim _{\Delta t \rightarrow 0} \frac{\Delta C}{\Delta t}\)

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