The approximate rate of change in the number of subscribers to wireless service
is given by f’(t) = 1.498t + 1.626, where t represents the number of years since 1990. In 1992
(t = 2) there were approximately 8.893 million subscribers.
Find the function that gives the total number of wireless service subscribers in year t.
I have a hunch that f is in MILLIONS
f(t)= (1/2)(1.498) t^2 + 1.626 t + c
to find c put in year 2
8.893 = (1/2)(1.498) (4) + 1.626 (2) + c
To find the function that gives the total number of wireless service subscribers in year t, we need to integrate the rate of change function f'(t).
Given that f'(t) = 1.498t + 1.626, we need to find the antiderivative of this function to get the total number of subscribers.
The antiderivative of 1.498t is (1.498/2)t^2 = 0.749t^2, and the antiderivative of 1.626 is 1.626t.
So the antiderivative of f'(t) = 0.749t^2 + 1.626t.
To find the constant of integration, we need an initial condition. In this case, we know that in 1992 (t = 2), there were approximately 8.893 million subscribers. So we can substitute this information into the antiderivative equation:
0.749(2)^2 + 1.626(2) + C = 8.893 million
2.996 + 3.252 + C = 8.893 million
C = 8.893 million - 2.996 - 3.252
C = 2.645 million
Therefore, the function that gives the total number of wireless service subscribers in year t is:
f(t) = 0.749t^2 + 1.626t + 2.645 million