a website is offering a promotion, during which customers can buy up to 100 photos for a flat fee. the cost per photo varies inversely with the number of photos a customer buys, as shown in the table below. what function models the data?
Number of photos 20/40/50/80
Cost per photo in cents 5/2.5/2/1.25
A. nc=25
B. nc=50
C. nc=100
D. nc=400
To find the function that models the data, we need to find the relationship between the number of photos (n) and the cost per photo (c). Since the cost per photo varies inversely with the number of photos, we can write the equation:
n * c = k
where k is a constant.
Let's use the given data to solve for k:
When n = 20, c = 5
20 * 5 = k
k = 100
So the equation becomes:
20c = 100
Similarly, for the other data points:
40 * 2.5 = 100
50 * 2 = 100
80 * 1.25 = 100
Since all the data points satisfy the equation, the function that models the data is:
nc = 100
Therefore, the correct answer is B. nc = 50.