Question

The revenue R you receive for selling pizza slices depends on the price p that you charge per slice and is modeled by R =-16p

Answer 1

Answer:

$p \geq 0$

Step-by-step explanation:

Given

$R(p) = -16p^2 + 80p + 5$

Required

Determine the domain of the function

To do this, we need to solve for the vertex, p of the function

$p= \frac{-b}{2a}$

Given the the general form of a quadratic function is:

$y = ax^2 + bx + c$

By comparison, we have:

$a = -16$    $b =80$    $c = 5$

So:

$p= \frac{-b}{2a}$

$p = \frac{-80}{-16 * 5}$

$p = \frac{-80}{-80}$

$p = 1$

Substitute 1 for p in $R(p) = -16p^2 + 80p + 5$

$R(1) = -16(1)^2 + 80(1) + 5$

$R(1) = -16 + 80 + 5$

$R(1) = 69$

This implies that

$(p, R) = (1,69)$

The interpretation of this is that;

For every value of p, there's a corresponding value of R.

However, because p indicates price and it's impossible to have a negative price, we can say that the minimum value of p is 0;

Hence, the domain is

$p \geq 0$