A certain organism population in a laboratory dish changes at a rate modeled by where…
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
A certain organism population in a laboratory dish changes at a rate modeled by
P′(t)=5e0.3t−20
where P′(t) is measured in cells per hour and t is the time in hours after the beginning of observation. At time t=0 the population is 800 cells.
(a) Determine the time t>0 at which the population transitions from decreasing to increasing. Show analytical work.
(b) Calculate the net change in the population during the first 6 hours.
(c) Find an explicit expression for the population P(t) for 0≤t≤6.
(d) At t=6, compute the average population over the interval 0≤t≤6 and interpret this value in context.