A population of bacteria doubles every hour, but 1.0 x 106 individuals are removed after reproduction to be converted into valuable biological by-products. The population begins with b0 = 3.0 x 106 bacteria.
a. Find the population after 1, 2, and 3 hours.
b. How many bacteria were harvested?
c. Write the discrete-time dynamical system.
d. Suppose you waited to harvest bacteria until the end of 3 hours. How many could you remove and still match the population b3 found in part a? Where did all the extra bacteria come from?
Follow the steps to derive discrete-time dynamical systems describing the above contrasting situations.