tropical pools sells an above ground model for p dollars each the monthly revenue for this model is given by the formula R(p)=-0.08p^2+300p
revenue is the product of the price p and the demand(quanity sold)
a.) factor out the price on the right hand side of the formula
b.) write a formula D(p)for the monthly demand
a) To factor out the price on the right hand side of the formula, we can rewrite the formula as follows:
R(p) = p(-0.08p + 300)
We have factored out the price (p) on the right hand side by taking it out as a common factor.
b) To write a formula for the monthly demand (D(p)), we need to solve the equation for p in terms of R(p). Let's rearrange the equation accordingly:
R(p) = -0.08p^2 + 300p
We can start by factoring out -0.08 as a common factor:
R(p) = -0.08(p^2 - 3750p)
Next, divide each term by -0.08 to isolate (p^2 - 3750p):
R(p)/(-0.08) = p^2 - 3750p
Now, let's rearrange the equation to have the terms in the standard form for a quadratic equation:
p^2 - 3750p - R(p)/(-0.08) = 0
The quadratic equation is of the form ax^2 + bx + c = 0, where a = 1, b = -3750, and c = -R(p)/(-0.08). Therefore, the formula for monthly demand (D(p)) is the quadratic equation:
D(p) = p^2 - 3750p - R(p)/(-0.08)