Question

The total sales of S (in thousands of DVD's) of a certain movie are given by the following formula where t is the number of months since the release of the DVD. Use the formula to answer the questions. S(t)=

t
2
+150
90t
2

​
a) Find S
′
(t). S
′
(t)=
(t
2
+50)
2

9,000t
​
b) Find S(15) and S
′
(15) The value of S(15) rounded to the nearest hundredth is The value of S
′
(15) rounded to the nearest hundredth is The total sales of S (in thousands of DVD's) of a certain movie are given by the following formula where t is the number of months since the release of the DVD. Use the formula to answer the questions. S(t)=
t
2
+150
90t
2

​
What do the values for S(15) and S
′
(15) indicate? A. After 15 months, the total sales are 2880 DVD's and the sales are increasing at the rate of 54 DVD's per month. B. After 15 months, the total sales are 28,800 DVD's and the sales are increasing at the rate of 5400 DVD's per month. C. After 15 months, the total sales are 54,000 DVD's and the sales are increasing at the rate of 2880 DVD's per month. D. After 15 months, the total sales are 54,000 DVD's and the sales are increasing at the rate of 2.88 DVD's The total sales of S (in thousands of DVD's) of a certain movie are given by the following formula where t is the number of months since the release of the DVD. Use the formula to answer the questions. S(t)=
t
2
+150
90t
2

​
C. After 15 months, the total sales are 54,000 DVD's and the sales are increasing at the rate of 2880 DVD's per month. D. After 15 months, the total sales are 54,000 DVD's and the sales are increasing at the rate of 2.88 DVD's per month. c) Use the results from part (b) to estimate the total sales after 16 months. After 16 months, the total sales will be approximately how many DVD's? (Round to the nearest whole number.)

Answer 1

a) Find S′(t).

`S′(t) = (t^2 + 50)/(9,000t)`

b) Find S(15) and S′(15).

S(15) = 2,880.00 DVD's

S′(15) = 54.00 DVD's/month

How to solve

c) Use the results from part (b) to estimate the total sales after 16 months.

After 16 months, the total sales will be approximately 2,934 DVD's. (Round to the nearest whole number.)

What do the values for S(15) and S′(15) indicate?

The value of S(15) = 2,880.00 DVD's indicates that after 15 months, the total sales of the movie have reached 2,880,000 DVD's. The value of S′(15) = 54.00 DVD's/month indicates that the rate of sales of the movie is increasing at 54 DVD's per month.