Question

A company produces custom greeting cards. The cost c (in dollars) of producing n greeting cards per month can be modeled by the function c = 480 + 1.25n. Find the inverse of the model.

Answer 1

The inverse of the cost function c = 480 + 1.25n is found by isolating n and expressing it as a function of c, resulting in n(c) = (c - 480) / 1.25.

Step-by-step explanation:

To find the inverse of the function c = 480 + 1.25n, which models the cost of producing n greeting cards per month, we need to solve for n in terms of c. This involves switching the dependent and independent variables and solving for the new independent variable.

Starting with the original function:

• c = 480 + 1.25n

We first subtract 480 from both sides to isolate the term containing n:

• c - 480 = 1.25n

Then, divide both sides of the equation by 1.25 to solve for n:

• (c - 480) / 1.25 = n

Now, we express this as a function of c:

• n(c) = (c - 480) / 1.25

This equation represents the inverse function, where n is the number of greeting cards that can be produced for a given cost c.