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

To find the saturation point, we need to look at the limit of the function as t approaches infinity. This limit can be found by dividing the leading coefficient of the highest degree term (in this case, 30,000) by the leading coefficient of the second-highest degree term (in this case, 11). Therefore, the saturation point is 30,000/11 = 2727.27 (rounded to the nearest whole number), or approximately 3,000 units.

To find the number of units sold after 5 years, we substitute t = 5 into the equation: 
11(5^3) + 600(5^2) + 1500(5) + 5000 = 18,067.

Therefore, the correct answer is C: The saturation point for the market is 30,000 units and 17,944 units will be sold after 5 years.

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

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