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DM
Numerade Educator

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Problem 13 Easy Difficulty

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

(a) $C^{\prime \prime}(t)$ is the instantancous rate of change of percentage of full capacity with respect to elapsed time in hours.
(b) The graph of $C^{\prime}(t)$ tells us that the rate of change of percentage of full capacity is decreasing and approaching 0

Discussion

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CA

Catherine A.

October 23, 2020

This will help alot with my midterm

SA

Sharieleen A.

October 26, 2020

Daniel J, thanks this was super helpful.

Video Transcript

So in this problem were given a rechargeable battery being plugged into a charger and we're giving this graph for C. Of T. Which is the percent of full charge the battery reaches as a function of time. And were asked a series of questions here. Right. First of all we're asked the meaning of the derivative. See prime of T. Well, what does that mean? First of all, what is the derivative derivative? Is the slope of this curve which is the rate of change of percent of full charge over time. Mhm. Okay then we're asked to sketch the graph of CFT. And what does the graph tell you? Well, I do the graph of C. Of T. Right here. See prime of T. Excuse me. Okay. So we start out this is a very positive slope isn't it? And it tends toward zero as we get further and further up this curve. So that means that this curve go something like this, doesn't it? Where again this is in T hours and this is percent of full charge. Okay. And what does it tell us, tells us that we get a lot of charge to start with, lot of charge at the start and I should say a lot of change in the charge at the start and it trends board zero. Right? Because down here at the end we are at nearly zero and trending toward it