The formula for the milligrams of bacteria in a certain population as a function of t in hours is described as: P(t) = 300 3 + 97e 0.2t mg of bacteria.

-What are the equations of: P, P , and P ?

-Describe the local maxima, minima, and points of inflection, if applicable.

-What is the asymptotic behavior of this function? That is, what does the function look like for massive t, at t = 1000.

-When, if at all, does the population become 20mg?

-When, if at all, does the population become 200mg?

-At what time is the population growing the fastest and what is the amount of the population?

-If the population has a limiting value, when is it within 1mg of that limit?

-List the doubling times of the population relative to the starting value.

Thanks!