A company uses the function C(x)= 20.50x+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.
C = 20.50x + 2000 = $625,000.
20.5x = 625000 - 2000 = 623000
X = 30,390 Units,
To find the inverse of the function, we need to interchange the roles of C and x and solve for x.
The original function is C(x) = 20.50x + 2000.
Step 1: Replace C(x) with x and x with C:
x = 20.50C + 2000
Step 2: Solve for C by isolating it on one side of the equation:
x - 2000 = 20.50C
Step 3: Divide both sides of the equation by 20.50 to solve for C:
C = (x - 2000) / 20.50
Therefore, the inverse function is C^(-1)(x) = (x - 2000) / 20.50.
Now, to determine the number of units produced when the cost is $625,000, we substitute C = $625,000 into the inverse function and solve for x:
C^(-1)(x) = ($625,000 - 2000) / 20.50
C^(-1)(x) = $622,000 / 20.50
C^(-1)(x) ≈ 30,341.46
Therefore, approximately 30,341.46 units are produced when the cost is $625,000.