Explanation

To answer this question, it is important to understand what is meant by the phrase “directly proportional.”

It means that \(a = kb\), where k is a constant.

In alternative form: = k, where k is a constant.

So, because they both equal the constant, \(\frac{a_{old}}{b_{old}}=\frac{a_{new}}{b_{new}}\). Plugging in values: \(\frac{8}{2}=\frac{a_{new}}{4}\).
Crossmultiply and solve:
\(32 = 2a_{new}\)
\(a_{new} = 16\)

We have two scenarios

\(b^3 = a\) \((2^3 = 8)\)

and

\(4b = a\) \((4*2 = 8)\)

Since the problem contains the words "directly proportional",

we must choose the second scenario and not the first. In other words, the graph should be a straight line and not an exponential curve.

So, if \(b=4\), then the value of a must be \(4*4 = 16\). Choice B

The exponential relationship will give us \(4^3 = 64\), which is there as a trap answer.