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question 6
consider the revenue function
$r(p)=-2p^{2}+40p$
where $r$ is the revenue (in dollars) and $p$ is the associated unit price. which of the following best describes the implied domain of this model?
0,10
nothing in this list is correct.
0,200
0,20
$(-\infty,\infty)$

Explanation:

Step1: Analyze real - world context

In a revenue - price model, price $p\geq0$. Also, revenue $R(p)\geq0$. Set $R(p)= - 2p^{2}+40p = 0$.

Step2: Solve the quadratic equation

Factor out $- 2p$: $-2p(p - 20)=0$. So $p = 0$ or $p = 20$. The parabola $y=-2p^{2}+40p$ opens downwards (because the coefficient of $p^{2}$ is negative, $a=-2<0$). The function $R(p)\geq0$ when $0\leq p\leq20$.

Answer:

$[0,20]$