the total sales of s (in thousands of dvds) of a certain movie are given by the following formula where t is…

the total sales of s (in thousands of dvds) 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)=\frac{80t^{2}}{t^{2}+100} a) find s(t). s(t)=\frac{16000t}{(t^{2}+100)^{2}} b) find s(5) and s(5). the value of s(5) rounded to the nearest hundredth is 16.00. the value of s(5) rounded to the nearest hundredth is .

the total sales of s (in thousands of dvds) 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)=\frac{80t^{2}}{t^{2}+100} a) find s(t). s(t)=\frac{16000t}{(t^{2}+100)^{2}} b) find s(5) and s(5). the value of s(5) rounded to the nearest hundredth is 16.00. the value of s(5) rounded to the nearest hundredth is .

Answer

Explanation:

Step1: Recall the formula for $S'(t)$

We know $S'(t)=\frac{16000t}{(t^{2}+100)^{2}}$.

Step2: Substitute $t = 5$ into $S'(t)$

Substitute $t = 5$ into the derivative formula: [ \begin{align*} S'(5)&=\frac{16000\times5}{(5^{2}+100)^{2}}\ &=\frac{80000}{(25 + 100)^{2}}\ &=\frac{80000}{125^{2}}\ &=\frac{80000}{15625}\ & = 5.12 \end{align*} ]

Answer:

$5.12$