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.
Upper S left parenthesis t right parenthesis equals StartFraction 40 t squared Over t squared plus 150 EndFractionS(t)=40t2t2+150
Question content area bottom
Part 1
a) Find
Upper S prime left parenthesis t right parenthesisS′(t).
Upper S prime left parenthesis t right parenthesisS′(t)equals=enter your response here
Part 2
b) Find
Upper S left parenthesis 15 right parenthesisS(15)
and
Upper S prime left parenthesis 15 right parenthesisS′(15).
The value of
S(1515)
rounded to the nearest hundredth is
enter your response here.
Part 3
The value of
Upper S prime left parenthesis 15 right parenthesisS′(15)
rounded to the nearest hundredth is
enter your response here.
Part 4
What do the values for
Upper S left parenthesis 15 right parenthesisS(15)
and
Upper S prime left parenthesis 15 right parenthesisS′(15)
indicate?
A.
After
1515
months, the total sales are
12 comma 80012,800
DVD's and the sales are increasing at the rate of
24002400
DVD's per month.
B.
After
1515
months, the total sales are
24 comma 00024,000
DVD's and the sales are increasing at the rate of
12801280
DVD's per month.
C.
After
1515
months, the total sales are
24 comma 00024,000
DVD's and the sales are increasing at the rate of
1.281.28
DVD's per month.
D.
After
1515
months, the total sales are
12801280
DVD's and the sales are increasing at the rate of
2424
DVD's per month.
Part 5
c) Use the results from part (b) to estimate the total sales after
1616
months.
After
1616
months, the total sales will be approximately how many DVD's?