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) = 80t^2 / (t^2 + 100) a) Find S'(t). S'(t) = b) Find S(20) and S'(20). The value of S(20) rounded to the nearest hundredth is . The value of S'(20) rounded to the nearest hundredth is . What do the values for S(20) and S'(20) indicate? A. After 20 months, the total sales are 64,000 DVD's and the sales are increasing at the rate of 1.28 DVD's per month. B. After 20 months, the total sales are 12,800 DVD's and the sales are increasing at the rate of 6400 DVD's per month. C. After 20 months, the total sales are 1280 DVD's and the sales are increasing at the rate of 64 DVD's per month. D. After 20 months, the total sales are 64,000 DVD's and the sales are increasing at the rate of 1280 DVD's per month. c) Use the results from part (b) to estimate the total sales after 21 months. Click to select your answer(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) = 80t^2 / (t^2 + 100)

a) Find S'(t).
S'(t) = 

b) Find S(20) and S'(20).
The value of S(20) rounded to the nearest hundredth is .
The value of S'(20) rounded to the nearest hundredth is .

What do the values for S(20) and S'(20) indicate?

A. After 20 months, the total sales are 64,000 DVD's and the sales are increasing at the rate of 1.28 DVD's per month.
B. After 20 months, the total sales are 12,800 DVD's and the sales are increasing at the rate of 6400 DVD's per month.
C. After 20 months, the total sales are 1280 DVD's and the sales are increasing at the rate of 64 DVD's per month.
D. After 20 months, the total sales are 64,000 DVD's and the sales are increasing at the rate of 1280 DVD's per month.

c) Use the results from part (b) to estimate the total sales after 21 months.

Click to select your answer(s).

Show more…

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) = 80t^2 / (t^2 + 100)

a) Find S'(t).
S'(t) =

b) Find S(20) and S'(20).
The value of S(20) rounded to the nearest hundredth is .
The value of S'(20) rounded to the nearest hundredth is .

What do the values for S(20) and S'(20) indicate?

A. After 20 months, the total sales are 64,000 DVD's and the sales are increasing at the rate of 1.28 DVD's per month.
B. After 20 months, the total sales are 12,800 DVD's and the sales are increasing at the rate of 6400 DVD's per month.
C. After 20 months, the total sales are 1280 DVD's and the sales are increasing at the rate of 64 DVD's per month.
D. After 20 months, the total sales are 64,000 DVD's and the sales are increasing at the rate of 1280 DVD's per month.

c) Use the results from part (b) to estimate the total sales after 21 months.

Click to select your answer(s).

Added by Rodrigo M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Shaiju T

03/25/2022

Step 1

Step 1: Find S'(t) Given: \(S(t) = \frac{80t^2}{t^2 + 100}\) Using the quotient rule of differentiation, we have: \[S'(t) = \frac{160t(t^2 + 100) - 80t^2(2t)}{(t^2 + 100)^2}\] \[S'(t) = \frac{160t^3 + 16000t - 160t^3}{(t^2 + 100)^2}\] \[S'(t) = \frac{16000t}{(t^2 Show more…

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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) = 80t^2 / (t^2 + 100) a) Find S'(t). S'(t) = b) Find S(20) and S'(20). The value of S(20) rounded to the nearest hundredth is . The value of S'(20) rounded to the nearest hundredth is . What do the values for S(20) and S'(20) indicate? A. After 20 months, the total sales are 64,000 DVD's and the sales are increasing at the rate of 1.28 DVD's per month. B. After 20 months, the total sales are 12,800 DVD's and the sales are increasing at the rate of 6400 DVD's per month. C. After 20 months, the total sales are 1280 DVD's and the sales are increasing at the rate of 64 DVD's per month. D. After 20 months, the total sales are 64,000 DVD's and the sales are increasing at the rate of 1280 DVD's per month. c) Use the results from part (b) to estimate the total sales after 21 months.

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00:01 In this problem, we are told that the total sales of a certain movie is given by the function s of t equal to 80 t squared divided by t squared plus 100, where t is the number of months since the release of the movie.

00:13 Now, here for the first part of the problem, we have to find a differential of s with respect to t, that means s dash of t, which will be given by d divided by dt of 80t of 80 square divided by t square plus 100, using the question rule of difference.

00:30 We get t square plus hundred multiplied by the differentiation of 80 t square that will be 160 t minus 80 t squared multiplied by the differentiation of t square plus hundred that is equal to two t whole divided by t square plus hundred square from here in the next step we get 160 multiplied by t multiplied by t squared plus hundred minus t squared divided by t square plus hundred square so from here we get the value of s dash of t equal to 160 sorry one 16 000 t divided by t square plus hundred square so this is the answer to the first part of the problem for part b we have to find the values of s of 20 and s dash of 20 so first we will find the value of s of 20 that will be given by substituting the value of 20 of t equal to 20 in the given function so here we get 80 multiplied by 20 square divided by 20 square plus 100 and after solving this we get it equal to 64 next we will find the value of s dash of 20 here also we will substitute t equal to 20 in its formula so we will write 16 000 multiplied by t squared that means 20 sorry multiplied by t that is 20 divided by t square that means 20 square plus hundred whole square and on solving this we get it equal to 1 .28 and these values indicates that after 20 months the sales value is 64 ,000 sorry these are the total number of sales are 64 ,000 and the sales increasing at a rate of 1 .28 dvds per month.

02:56 So this is the answer to part b of the problem...

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