Answer:
The average sales per week for the first 16 weeks is $477 million dollars per week.
Step-by-step explanation:
Here, you have to find the average value of a continuous function over an interval.
Suppose you have a function [tex]f(x)[/tex] over an interval from a to b. The average of the function in this interval is given by:
[tex]\frac{1}{b-a}\int\limits^b_a {f(x)} \, dx[/tex]
Solution:
In this problem, the function is given by:
[tex]S(t) = 59t + 5[/tex]
The problem asks the average value for the first 16 weeks. It means that our interval goes from 0 to 16. So [tex]a = 0, b = 16[/tex].
The average value is given by the following integral:
[tex]A = \frac{1}{16}\int\limits^{16}_{0} {(59t + 5)} \, dt[/tex]
[tex]A = \frac{59t^{2}}{32} + \frac{5t}{16}, 0 \leq t \leq 16[/tex]
[tex]A =\frac{59*(16)^{2}}{32} + \frac{5*16}{16}[/tex]
[tex]A = $477[/tex]
The average sales per week for the first 16 weeks is $477 million dollars per week.
