The cumulative sales (in thousands of units)of a new product after it has been on the market for t years may be modeled by During the first year,5000 units were sold.What is the saturation point for this product? How many units will be sold after 5 years?
A) The saturation point for the market is 3,000 units and 17,944 units will be sold after 5 years.
B) The saturation point for the market is 30,000 units and 26,049 units will be sold after 5 years.
C) The saturation point for the market is 30,000 units and 17,944 units will be sold after 5 years.
D) The saturation point for the market is 30,000 units and 18,067 units will be sold after 5 years.
E) The saturation point for the market is 3,000 units and 26,049 units will be sold after 5 years.

Question

​The cumulative sales (in thousands of units)of a new product after it has been on the market for t years may be modeled by  During the first year,5000 units were sold.What is the saturation point for this product? How many units will be sold after 5 years? ​
A) ​The saturation point for the market is 3,000 units and 17,944 units will be sold after 5 years. 
B) ​The saturation point for the market is 30,000 units and 26,049 units will be sold after 5 years. 
C) ​The saturation point for the market is 30,000 units and 17,944 units will be sold after 5 years. 
D) ​The saturation point for the market is 30,000 units and 18,067 units will be sold after 5 years. 
E) ​The saturation point for the market is 3,000 units and 26,049 units will be sold after 5 years.

Quizplus · Accepted Answer

The given function is 11ea8970_6a09_efcf_861b_afd694cb7dc0_TB1301_11

To find the saturation point, we need to find the limit of the function as t approaches infinity.

lim as t→∞ 11ea8970_6a09_efcf_861b_afd694cb7dc0_TB1301_11 = 30,000

So, the saturation point for the market is 30,000 units.

To find the number of units sold after 5 years, we substitute t = 5 into the function:

11ea8970_6a09_efcf_861b_afd694cb7dc0_TB1301_11 = 5000 + 10000(1 - e^(-0.1*5))

= 5000 + 10000(1 - e^(-0.5))

= 17,944 (rounded to the nearest whole number)

Therefore, the number of units sold after 5 years is 17,944.

So, the best choice is C.

​The Cumulative Sales (In Thousands of Units)of a New Product

The Cumulative Sales (In Thousands of Units)of a New Product