Question

The total sales Slin thousands of CD's. J for the Compact disk given!
SCEJ
90t²
t²+50
Where t is the number of months since the release of the CD's
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Answer 1

The total sales S (in thousands of CD's) for a compact disk are given by: 90t2 t2 + 50 S(t) = Where t is the number of months since the release of the CD. Find S(10) and S'(10). Write a brief verbal interpretation of these results. Use the result from part (ii) to estimate the total sales of these results.

MARK ME AS BRAINLIST......

Answer 2

Answer:

Step-by-step explanation:

To find S(10), we plug t = 10 into the given equation:

S(10) = 90(10)^2 / (10)^2 + 50 = 9,050

To find S'(10), we first differentiate the given equation with respect to t:

S(t) = 90t^2 / (t^2 + 50)

S'(t) = [180t(t^2+50) - 90t^2(2t)] / (t^2+50)^2

= 90t(50 - t^2) / (t^2 + 50)^2

Then we plug t = 10 into this derivative:

S'(10) = 90(10)(50 - 10^2) / (10^2 + 50)^2 = -1.2245

The interpretation of these results is as follows:

S(10) represents the total sales (in thousands of CDs) of the CD 10 months after its release.

S'(10) represents the instantaneous rate of change of total sales with respect to time (in thousands of CDs per month) when t = 10 months. The negative value of S'(10) indicates that the total sales is decreasing at a rate of approximately 1,224 CDs per month at the 10th month after its release.

(ii)

We can use S'(10) to estimate the total sales for a short period of time after the 10th month. Assuming that the instantaneous rate of change remains constant, we can use the formula:

ΔS ≈ S'(10) Δt

where ΔS is the change in total sales (in thousands of CDs), and Δt is the time interval (in months).

For example, if we want to estimate the total sales for the next 2 months (i.e. Δt = 2), we have:

ΔS ≈ S'(10) Δt = -1.2245 x 2 = -2.449

This means that we expect the total sales to decrease by approximately 2,449 CDs over the next 2 months after the 10th month. To estimate the new total sales after the 2 months, we subtract ΔS from S(10):

S(10+2) ≈ S(10) - ΔS = 9,050 - (-2.449) = 9,052.449

Therefore, we estimate that the total sales of the CD will be approximately 9,052,449 (in thousands of CDs) at the 12th month after its release.