Question

Indicate whether the following statement is true or false: An exponential growth function eventually exceeds a quadratic function with a positive leading coefficient.

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
`2^(x)` and a quadratic function
`200 x^(2) +150x+500`.

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.

Answer 2

In the given statement, "An exponential growth function eventually exceeds a quadratic function with a positive leading coefficient." the statement is correct. An nth degree polynomial “turns around” at most n - 1 times (where n is a positive integer), but there may be fewer turns which can be seen as well in an exponential growth function.