2. Consider a simple pendulum that has a length of 50 cm and a maximum horizontal displacement of 8 cm.

a) Find the period of the pendulum.

b) Determine a function that gives the horizontal position of the bob as a function of time.

c) Determine a function that gives the velocity of the bob as a function of time.

d) Determine a function that gives the acceleration of the bob as a function of time.

3. A fruit fly infestation is doubling every day. There are ten flies when the infestation is first discovered.

a) Write an equation that relates the number of flies to time.

b) Determine the number of flies present after 1 week.

c) How fast is the fly population increasing after 1 week?

d) How long will it take for the fly population to reach 500?

e) How fast is the fly population increasing at this point?