In this part of the task on rates of this part of the task, students will complete rates of change of

exponential growth in a biotechnology case study.

A simplified model for bacterial growth is where P(t) = P 0 e rt where P(t) is the population of the

bacteria colony after (t) hours, P 0 is the initial population of the colony (the population at t=0),

and (r) determines the growth rate of the colony. This model is simple in that it does not account

for limited resources, such as space and nutrients. In this model, as time increases, so does the

population, but there is no bound on the population.

To determine how the population of a particular type of bacteria will grow overtime under

controlled conditions, a microbiologist observes the initial population and the population every

half hour for 8 hours.

After analyzing the population data, the microbiologist determines that the population of the

bacteria colony can be modeled by the equation:

P(t) = 500e 0.1t

a. What is the initial population of the bacteria colony?

K/U

b. What function describes the instantaneous rate of change in the bacteria population after (t)

hours?

T/I

c. Plot a graph between the populations of the bacteria and time (t). What is the instantaneous

rate of change of the population after 1h? What is the instantaneous rate of change after 8h?

COMM, K/U

d. How does your answer to c. help you in making a prediction about how long it will take for

the bacteria colony to double in size? Make a prediction for the number of hours it will take the

population to double, using the answers to c. and/or other information.

APP

e. Determine the actual doubling time, the time that it takes the colony to grow to twice its initial

population. (Hint: solve for (t) when P(t) = 1000)

T/I

f. Compare your prediction for the doubling time to the calculated value. If your prediction was

not close to the actual value, what factors do you think might account for the difference?

COMM

g. When is the instantaneous rate of change equal to 500 bacteria/h?

APP