Question

The rate of sales for a corporation t weeks from now is given by S(t)=59t+5 millions of dollars per week. Find the average sales per week for the first 16 weeks. Set up the integral to solve the problem and express your answer to the nearest dollar.

Answer 1

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 $f(x)$ over an interval from a to b. The average of the function in this interval is given by:

$\frac{1}{b-a}\int\limits^b_a {f(x)} \, dx$

Solution:

In this problem, the function is given by:

$S(t) = 59t + 5$

The problem asks the average value for the first 16 weeks. It means that our interval goes from 0 to 16. So $a = 0, b = 16$.

The average value is given by the following integral:

$A = \frac{1}{16}\int\limits^{16}_{0} {(59t + 5)} \, dt$

$A = \frac{59t^{2}}{32} + \frac{5t}{16}, 0 \leq t \leq 16$

$A =\frac{59*(16)^{2}}{32} + \frac{5*16}{16}$

$A = 477$

The average sales per week for the first 16 weeks is $477 million dollars per week.