Question

The answer key says the answer is B, but I don't understand how it is decreasing...isn't the velocity shown to be increasing? And if it is decreasing, then how come with exponential graphs we were taught this would be a growth function?

Answer 1

Answer:

Acceleration and velocity are two different things.  The acceleration is the rate at which the velocity is increasing.  So while the velocity very well may be increasing, the rate (acceleration) at which it is, is decreasing.

Answer 2

Explanation:

The curve shows velocity, which is increasing from left to right, except perhaps at the very end, where it appears to be constant.

The question asks about acceleration, which is the derivative of velocity. On a graph like this, acceleration is the slope of the velocity curve.

The slope starts out steep (very much positive) and ends up flat (very near zero). Hence the slope (acceleration) is decreasing.

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An exponential function is concave upward (when it is above the horizontal asymptote). This function is concave downward. It is not an exponential growth function.

An exponential decay function can look like this if it is vertically shifted upward. This one comes to what looks like zero slope, which an exponential function never does.