A model incorporating growth restrictions for the number of bacteria in a culture after t days is given by f (t) = 5000(20 + te-0.04t).

(a) Graph f′(t) and f′′(t) in the window [0, 100] by [-700, 300].

(b) How fast is the culture changing after 100 days?

(c) Approximately when is the culture growing at the rate of 76.6 bacteria per day?

(d) When is the size of the culture greatest?

(e) When is the size of the culture decreasing the fastest?