(need help answering #3 only!!! for the first two problems I included the answers)

Question

The population of bacteria in one cubic centimeter of the blood of a sick person has been modeled by the function P(t)=115t(0.75t) where t is the time, in days, since the person became ill.
Use your calculator to graph the function.
Then use the graph to answer the following questions:
1. To the nearest day, when is the bacteria population at a maximum? Day: 3
2. What is the maximum population? Round your answer to one decimal place. Population: 147.059
3. Estimate how fast the population is changing 14 days after the onset of the illness. Round your answer to two decimal places. Rate of Change:

Answer 1

I have a valid suspicion that P(t)=115t(0.75t)
is supposed to be P(t)=115t(0.75^t), your calculations reflected that.

P'(t) = (115t)(.75^t)(ln.75) + 115(.75^t)
= 0 for a max
(115t)(.75^t)(ln.75) = -115(.75^t)
tln.75 = -1
t = -1/ln.75 = 3.48 , or 3 to the nearest day, you had that, Great!

2) you are correct, I had the same correct to 3 decimals

3) Don't know what your course understands by "estimate".
To me it means: do your work in your head with as little "paperwork" as
possible. Definitely no calculator. I don't know how that would be possible here.

rough work:
(100t)(3/4)^14 (ln.75) + 100(3/4)^t

actual answer: put t = 14 into the derivative

Answer 2

Thank you so much for your help!!!