The size P(t) of an isolated bacterial colony, measured in thousands of cells, is modeled by
P(t)=7.5t32,t≥0,
where t is measured in hours.
(a) Determine the instantaneous rate of growth of the colony at t=8 hours. Include correct units in your answer.
(b) Compute the average rate of growth of the colony over the time interval 0≤t≤8. Include units.
(c) Compare the results from parts (a) and (b). Explain, using complete sentences, what the comparison reveals about how the growth rate of the colony changes over time.