Question

Photo Necessities produces camera cases. They have found that the cost, (c(x)), of making (x) camera cases is a quadratic function in terms of (x). The company also discovered that it costs $23 to produce 2 camera cases, $103 to produce 4 camera cases, and $631 to produce 10 camera cases.

a. Determine the quadratic function (c(x)) in terms of (x).
b. Find the cost of producing 6 camera cases.
c. What is the significance of the quadratic term in the con of this problem?

Answer 1

We can determine the quadratic function (c(x)) in terms of (x) by using the given points and solving the resulting system of equations. Once we have the quadratic function, we can find the cost of producing 6 camera cases and analyze the significance of the quadratic term in the cost function.

Step-by-step explanation:

To determine the quadratic function (c(x)) in terms of (x), we can use the information provided. We have three points: (2, 23), (4, 103), and (10, 631). Using these points, we can set up three equations to solve for the coefficients of the quadratic function.

Let's start by assuming the quadratic function is of the form c(x) = ax^2 + bx + c. Substituting the first point (2, 23), we get 23 = 4a + 2b + c.

Similarly, substituting the second point (4, 103) and the third point (10, 631), we get two more equations. Solving these three equations simultaneously will give us the coefficients of the quadratic function c(x). Once we have the quadratic function, we can easily find the cost of producing 6 camera cases by substituting x = 6 in the function, and we can determine the significance of the quadratic term by analyzing its effect on the cost function.