In a controlled laboratory experiment, yeast cells are grown in an automated cell culture system that counts the number P of cells present at hourly intervals. The number after t hours is shown in the accompanying figure.

a. Explain what is meant by the derivative P′(5). What are its units?

b. Which is larger, P′(2) or P′(3)? Give a reason for your answer.

c. The quadratic curve capturing the trend of the data points is given by P(t) = 6.10t² - 9.28t + 16.43. Find the instantaneous rate of growth when t = 5 hours.

P 250 200 150 100 50 0 1 2 3 4 5 6 7