A bacterial culture has population P(t) cells at time t hours after it is first observed. The growth rate is modeled for 0≤t≤10 by
P′(t)=500e−0.2tcells per hour,
and the initial population is P(0)=2000 cells.
(a) Determine P(10), the number of cells in the culture 10 hours after observation began.
(b) Calculate the percentage increase in population over the first 10 hours.
(c) Find the average growth rate of the culture over the interval 0≤t≤10 and interpret your answer with units.