# what is the growth rate and continuous growth rate?

The problem: $\;f(t) = 4 \cdot 2^{\,t/5}$

I know continuous is e^k, but this problem doesn't seem to work for that. Is the initial value, 4, able to be used to find the growth rates?

-
The relative continuous growth rate of $f(t)$ is defined as $$\frac{f'(t)}{f(t)}.$$ Your function is $f(t)=4 \cdot 2^{t/5}$, with $f'(t)=4\cdot (1/5)\ln(2)2^{t/5}.$ So its relative growth rate is $(1/5)\ln(2)$. Note how the initial value 4 "cancelled out" in finding the relative continuous growth rate.
The growth rate is as I stated. It may be expressed as a percent, but that is irrelevant, since for example 30% means exactly the same as $30 \cdot \frac{1}{100}$ which is $.3$. –  coffeemath Dec 12 '12 at 9:03