population between times t = a and t = b is given by G(t) dt. The population
may consist of people, deer, fruit flies, bacteria, and so on.
Example 12 __
Suppose an epidemic is spreading through a city at the rate of f (t) new people
per week. Then
is the number of people who will become infected during the next 4 weeks (or
the total change in the number of infected people).
Example 13 __
Suppose a rumor is spreading at the rate of f (t) = 100e−0.2t new people per day.
Find the number of people who hear the rumor during the 5th and 6th days.
SOLUTION: people.
If we let F′(t) = f (t), then the integral above is the net change in F(t) from t = 4
to t = 6, or the number of people who hear the rumor from the beginning of the
5th day to the end of the 6th.
Example 14 __
Economists define the marginal cost of production as the additional cost of
producing one additional unit at a specified production level. It can be shown
that if C(x) is the cost at production level x then C′(x) is the marginal cost at that
production level.
If the marginal cost, in dollars, is per unit when x units are being produced,
find the change in cost when production increases from 50 to 75 units.
SOLUTION: