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)=□
Answer
Explanation:
Step1: Recall quotient - rule
The quotient - rule states that if $y=\frac{u}{v}$, then $y'=\frac{u'v - uv'}{v^{2}}$. Here, $u = 80t^{2}$, $u'=160t$, $v=t^{2}+100$, and $v' = 2t$.
Step2: Apply quotient - rule
[ \begin{align*} S'(t)&=\frac{(160t)(t^{2}+100)-80t^{2}(2t)}{(t^{2}+100)^{2}}\ &=\frac{160t^{3}+16000t - 160t^{3}}{(t^{2}+100)^{2}}\ &=\frac{16000t}{(t^{2}+100)^{2}} \end{align*} ]
Answer:
$\frac{16000t}{(t^{2}+100)^{2}}$