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?

A) There is not enough information to make a conclusion.

B) The linear function is growing faster, because at x = 3 the y-value of the linear function is larger.

C) The exponential function is growing faster, because at x = 0 the y-value of the exponential function is larger.

D) The exponential function is growing faster, because it grows by a factor that is multiplied by the previous y-value instead of being added like the linear function.

Answer 1

D) The exponential function is growing faster, because it grows by a factor that is multiplied by the previous y-value instead of being added like the linear function.

Explanation:

The rate of growth of a linear function is some constant. The rate of growth of an exponential function is unconstrained when the base of the exponential is more than 1, as it is here.

At some point, an exponential function will grow faster than a polynomial function of any degree. (A linear function is a polynomial function of degree 1.)