Question

A student draws portraits for customers. When the price of a picture is $180, the demand is 8 portraits. When the price of a picture is $100, the market is 24 portraits. Which graph best models the demand as a function of the cost? (Please show the steps on the graph)

Answer 1

Q = 216 - 0.5P

Explanation:

One approach to modeling the demand as a function of the cost is to use a linear demand equation of the form:

Q = a - bP

where Q is the quantity demanded, P is the price, and a and b are constants. To find these constants, we can use the two points given:

When P = $180, Q = 8 portraits, so 8 = a - b * 180

When P = $100, Q = 24 portraits, so 24 = a - b * 100

Solving the system of equations gives us:

a = 216

b = 0.5

So, the demand equation is:

Q = 216 - 0.5P

This represents the demand for portraits as a function of the price, where the demand decreases linearly as the price increases.