Question

Choose all that show that a quantity increasing exponentially eventually exceeds a quantity increasing linearly as x approaches infinity

Answer 1

A, B, C, D

Explanation:

First of all, logically, an exponential function should change faster than a linear function (linear functions increase/decrease at a constant rate while exponential functions increase/decrease at an increasing/decreasing rate). Thus, if an exponential function is growing, it increases faster than a linear function at one point. Also, looking at all of the graphs, note how every exponential function is able to surpass the linear function in height (y-values). This also shows how all of the exponential functions will exceed the linear functions.