A culture of bacteria has a population of 150 cells when it is first observed. The population doubles every 12 hr, which means its population is governed by the function p(t) = 150 ∙ 2^t/12, where t is the number of hours after the first observation.

a. Verify that p(0) = 150, as claimed.

b. Show that the population doubles every 12 hr, as claimed.

c. What is the population 4 days after the first observation?

d. How long does it take the population to triple in size?

e. How long does it take the population to reach 10,000?