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?A rechargeable battery is plugged into a charger. The graph shows C(t), the percentage
Chapter 2, Problem 13(choose chapter or problem)
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?
Questions & Answers
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.
\(C^{\prime}(t)=\lim _{\Delta t \rightarrow 0} \frac{\Delta C}{\Delta t}\)