Question

The table on the left is that of a linear function, and the one on the right is that of an exponential function. Can you tell which function has the higher rate of growth? How?

Answer 1

The correct answer is D.

As you can see, the exponential function grows by doubling the previous output with each increment of the input: start with 1, you double it to get 2, then you double it to get 4, 8 and so on.

On the other hand, the linear function adds 7 with each step. This means that the exponential function will eventually reach and pass the linear one, and will definitely be grater from that point on. In fact, if we continue the table, we get

`\begin{array}c\text{x value}&\text{linear}&\text{exponential}\\4&28&8\\5&35&16\\6&42&32\\7&49&64\\8&56&128\\9&63&256\end{array}`

and you can see how the exponential growth is much faster than the linear one.