12. The total number of people who have entered a museum
on a certain day is modeled by a function f(t), where t is measured in hours since the museum opened
that day. The total number of people who have left the museum since it opened that same day is
modeled by a function g(t). Both f(t)and g(t) are defined on the interval [1,10].
You are given that f'(t) = 380(1.02) and g'(t) = 240 + 240 sin (62).
a. Write a function that represents the rate at which the number of people in the museum is
changing at time t.