Question

Indicate whether the following statement is true or false: An exponential growth function

eventually exceeds a quadratic function with a positive leading coefficient. (1 point)
True
False

Answer 1

The given statement is true.

In general, the growth rate of exponential functions is far greater than the quadratic function. This can be illustrated through an example.

Consider an exponential function and a quadratic function .

Note that the leading coefficient of the quadratic function is far greater than the base of the exponential function but still the exponential function will exceeds the quadratic function after x = 15.664 as shown in the graph below.

Therefore, we can conclude that the given statement is correct.