48) This question asks us about charging a capacitor in an RC-circuit. We want to find the slope of the natural log. The way RC-circuits work is very interesting; if you are unfamiliar with RC-circuits, I highly recommend reading about them: First-Order RC and RL Transient Circuits.
First, let's write out the general form for current when charging a capacitor.
If we graph this equation we would find that current starts at some initial current and decreases exponentially as it comes to an assymptote at I[t] = 0.
Since we do not have enough information to find the initial current, and since the question only asks for the choice that best represents the curve, let's just write this as a proportionality.
Next, let's take the natural log of this function and simplify it.
Finally, taking the first derivative with respect to time we will find an equation for the slope.
Answer: D
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