
Exponential Growth
The count in a culture of bacteria was 400 after 2 hours and 25,600 after 6 hours.
(a) What is the relative rate of growth of the bacteria population?
(b) What was the initial size of the culture?
My big problem is how to find the rate of growth. Then when I find that I assume I plug in the rate and time=0 to find the initial size of the culture am I correct? I just don't know how to find that blasted rate of growth.

Let A be the initial size of the population, R be the growth rate per hour, and t be the time in hours. Let P represent the number of bacteria present. Then $\displaystyle P = AR^t$. We have $\displaystyle 400 = AR^2$ and $\displaystyle 25600 = AR^6$. Then:
$\displaystyle \frac{25600}{400} = \frac{AR^6}{AR^2} = R^4$.
Solve for R and then you can find A.

Hmm, I don't know how to solve for $\displaystyle R^4$ what am I doing with it? Modeling isn't exactly my strong suit, in fact its my worst. I'm sorry.

Bump because I don't understand.