Question

The population of bacteria in one cubic centimeter of the blood of a sick person has been modeled by the function P(t) = 80t(0.86^t) where t is the time, in days, since the person became ill.

I was able to answer all of the questions besides,
Estimate how fast the population is changing 5 days after the onset of the illness. Round your answer to two decimal places. Rate of Change:

Answer 1

P ' (t) = (80t)(.86^t)(ln .86) + 80(.86^t) , using the product rule and knowing that d(.86^t)/dt = ln(.86)(.86^t)

so if t = 5

P ' (5) = (400)(.86^5)(ln.86) + 80(.86^5)
= appr 9.25 people/day

check my arithmetic and calculator work

Answer 2

nothing