A company introduces a new product for which the number of units sold S is where t is the time in months since the product was introduced. During what month does equal the average value of during the first year?
A) October
B) July
C) December
D) April
E) March

Question

A company introduces a new product for which the number of units sold S is  where t is the time in months since the product was introduced. During what month does  equal the average value of  during the first year?
A) October 
B) July 
C) December 
D) April 
E) March

Quizplus · Accepted Answer

To find the average value of S during the first year, we need to evaluate:

(1/12) * integral from 0 to 12 of 11e^(0.08t) dt

Simplifying this integral, we get:

(1/12) * [11/0.08 * e^(0.08t)] from 0 to 12

= (11/0.08) * [e^(0.96) - 1]/12

= 85.64

To find the month where S equals the average value of S during the first year, we need to solve:

11e^(0.08t) = 85.64

Dividing both sides by 11 and taking the natural logarithm, we get:

0.08t = ln(85.64/11)

t = 11.053

Since t represents time in months, we can conclude that S equals the average value of S during the first year in April (the 12th month is equivalent to 0, so adding 11.053 to 12 gives a value just over 23, which corresponds to April of the second year). Therefore, the correct answer is (D) April.

A Company Introduces a New Product for Which the Number