The revenue for a business is modeled by the function R(x)=-2.8(x-10)^2+15, where x is the number of items sold, in thousands, and R(x) is the revenue in thousands of dollars. Express the number sold in terms of the revenue.
To express the number of items sold in terms of the revenue, we need to solve the revenue equation for x.
The given revenue function is R(x) = -2.8(x-10)^2 + 15.
We can start by isolating the variable x. Rearranging the equation, we have:
-2.8(x-10)^2 + 15 = R(x)
Next, let's move the constant term to the right side of the equation:
-2.8(x-10)^2 = R(x) - 15
To remove the coefficient -2.8, we divide both sides of the equation by -2.8:
(x-10)^2 = (R(x) - 15) / -2.8
Now, take the square root of both sides of the equation to solve for x:
√((x-10)^2) = ±√((R(x) - 15) / -2.8)
Remember to consider both the positive and negative square roots.
Simplifying the equation, we get:
x-10 = ± √((R(x) - 15) / -2.8)
Finally, re-arrange the equation to isolate x:
x = 10 ± √((R(x) - 15) / -2.8)
So, the number of items sold (x) is equal to 10, plus or minus the square root of (R(x) - 15) divided by -2.8.