MA 109 Applications of the Definite Integral

1) Suppose that an experiment is run in which bacteria are placed in a Petri dish.
It is observed that the number of bacteria initially drops and then starts to increase,
so that the number of bacteria N(t) is given by the following, where t is time in hours:

=

Find the average number of bacteria over the time interval from 0 to 30 hours.
Do the integration by hand and then verify the result by using your calculator.

2) Suppose that a retirement annuity pays $30,000 per year for 25 years. Assuming
that the current interest rate is 7%, what is the present value of this annuity at its
start (time 0)? Find the definite integral by hand, then verify with a calculator.