find the growth rate of f(x)=4e^2x

Question

I found the initial value and Y int. without an issue but the "e" is confusing me. If someone could help me with this that would be great.

Answer 1

Hello Joseph,

Let's do a slight, but significant re-write of f(x) so we end up with the typical exp function, i.e y = a*b^x

f(x) = 4 * e^2x = 4 * (e²)^x

Do you see now how your base "b" is equal to e²? e² is your growth factor. e² = 7.389..because it's greater than 1, it tells you this is exponential growth, not decay,

to find the growth/decay rate, you wanna do: growth rate = (growth factor - 1) * 100% = (e² -1)*100% = 6.389 *100% = 638.9%

It's positive, which confirms that it's exponential growth.

Recap: growth rate of f(x) = (e² - 1)*100% which approx equals 638.9%

Answer 2

Growth rate is f'(x) = 8e^2x > 0