In a study, a cancerous tumor was found to have a volume of f(t) = 1.825³(1 - 1.6e^-0.4196t)³ milliliters after t weeks, with t > 1.

(a) Sketch the graphs of f (t) and f′(t) for 1 ≤ t ≤ 15. What do you notice about the tumor’s volume?

(b) How large is the tumor after 5 weeks?

(c) When will the tumor have a volume of 5 milliliters?

(d) How fast is the tumor growing after 5 weeks?

(e) When is the tumor growing at the fastest rate?

(f) What is the fastest rate of growth of the tumor?