A new DVD is available for sale in a store one week after its release. The cumulative revenue, $R, from sales of the DVD in this store in we

Question

A new DVD is available for sale in a store one week after its release. The cumulative revenue, $R, from sales of the DVD in this store in week t after its release is R=f(t)=350 ln tR=f(t)=350lnt with t>1.
Find f(5), f'(5), and the relative rate of change f’/f at t=5. Interpret your answers in terms of revenue.

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bonexptip 4 years 2021-08-28T07:17:44+00:00 1 Answers 34 views 0

Answers ( )

  1. Xavia
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    2021-08-28T07:19:03+00:00
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    Solution :

    It is given that :

    $f'(t) = (350 \ln t)'$

           $=350(\ln t)'$

            $=\frac{350}{t}$

    So, f(5)=350 \ln (5) \approx 563

         $f'(5) = \frac{350}{5}$

                  =70

    The relative change is then,

    $\frac{f'(5)}{f(5)}=\frac{70}{350\ \ln(5)}$

             $=\frac{1}{5\ \ln(5)}$

             $\approx 0.12$

              =12\%

    This means that after 5 weeks, the revenue from the DVD sales in $563 with a rate of change of $70 per week and the increasing at a continuous rate of 12% per week.

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