A company uses the function C(x)=20.50+2000, where C is the cost and x is the number of units it produces, to determine its daily costs. Find the inverse of the function and determine how many units are produced when the cost is $625,000.
Where is x on the right ?
Sorry about that, it's 20.50x
3. Using proper grammar 1 point
3. What is the value of x + y? (5 points)
Rubrics:
1. Writing the correct equation(s) 1 point
2. Showing steps 1 point
3. Solving for x 1 point
4. Solving for y 1 point
5. Solving for x + y 1 point
To find the inverse of a function, we need to switch the roles of the independent and dependent variables. In this case, we want to find the inverse of the function C(x) = 20.50x + 2000, where C is the cost and x is the number of units produced.
Step 1: Replace C(x) with y.
y = 20.50x + 2000
Step 2: Switch the roles of x and y.
x = 20.50y + 2000
Step 3: Solve for y.
x - 2000 = 20.50y
(x - 2000)/20.50 = y
So, the inverse function is C^(-1)(x) = (x - 2000)/20.50.
To determine how many units are produced when the cost is $625,000, we need to substitute this cost into the inverse function and solve for x.
C^(-1)(x) = (x - 2000)/20.50
625,000 = (x - 2000)/20.50
To solve for x, we can cross-multiply and solve the resulting equation:
20.50 * 625,000 = x - 2000
x = 12,812,500 + 2000
x = 12,814,500
Therefore, when the cost is $625,000, the company produces approximately 12,814,500 units.