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 S(t) during the first year?
A)March
B)June
C)April
D)May
E)September

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 S(t) during the first year?
A)March 
B)June 
C)April 
D)May 
E)September

Quizplus · Accepted Answer

The first year would be the first 12 months, so we need to find the average value of S(t) over this interval.

We can find the total number of units sold during the first year by evaluating S(12) - S(0):

S(12) - S(0) = 11ec1854_fdac_26f7_acfc_df74e178abd0_TBX8702_11 - 11ec1854_fdac_26f7_acfc_bfb1332042e1_TBX8702_11

Simplifying this expression (using a calculator or other means) gives:

S(12) - S(0) = 1314

To find the average value of S(t) during the first year, we need to divide this total by the number of months in the first year:

average value = (1314) / (12) = 109.5

So we are looking for the month where S(t) = 109.5.

Solving the equation 11ec1854_fdac_26f7_acfc_df74e178abd0_TBX8702_11 = 109.5 gives:

t = 3.4643

Since t represents months, we can round up to the next integer to get the answer:

t = 4

Therefore, the month where 11ec1854_fdac_26f7_acfc_df74e178abd0_TBX8702_11 equals the average value of S(t) during the first year is April.

A Company Introduces a New Product for Which the Number