The cost of producing x bags of pretzels is modelled by C(x)=0.5x^2 + x + 2 where x=# of bags per hundred. State the function that represents the average cost.
Model average cost is C(x)/x. that is average cost per hundred.
2,8
To find the function that represents the average cost, we need to divide the total cost (C(x)) by the number of bags (x).
The average cost is calculated as:
Average Cost (AC) = Total Cost (C) / Number of Bags (x)
Substituting the given equation for total cost, C(x) = 0.5x^2 + x + 2, we can write the function for the average cost:
AC(x) = (0.5x^2 + x + 2) / x
We can simplify this expression further by dividing each term in the numerator by x:
AC(x) = (0.5(x^2/x) + (x/x) + (2/x))
Simplifying this expression gives us:
AC(x) = (0.5x + 1 + 2/x)
Therefore, the function that represents the average cost is AC(x) = 0.5x + 1 + 2/x.