A population of bacteria (in millions) is modeled for hours by P(t)= t^2 t+4
MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
A population of bacteria (in millions) is modeled for t≥0 hours by
P(t)=t+4t2.
Use this model to analyze population change.
(a) Determine P′(t) and express your answer in simplest rational form.
(b) Solve P′(t)=0 and identify all critical points of P for t≥0.
(c) Using a sign chart or equivalent reasoning, determine the intervals on which the population is increasing and the intervals on which it is decreasing.
(d) State the time at which the population attains its maximum value on [0,∞), and give that maximum population. Provide justification based on your work in parts (a)–(c).