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 (n) 20 40 50 80
Cost per photo in cents (c) 5 2.5 2 1.25
To find the function that models the data, we can first calculate the cost per photo for each quantity of photos.
For 20 photos:
c = 5 cents/photo
For 40 photos:
c = 2.5 cents/photo
For 50 photos:
c = 2 cents/photo
For 80 photos:
c = 1.25 cents/photo
From the data, we can see that as the number of photos increases, the cost per photo decreases. This relationship is an inverse relationship, as one increases the other decreases.
To find the function that models this inverse relationship, we can use the equation:
c = k/n
Where c is the cost per photo, k is a constant, and n is the number of photos.
We can use any pair of values from the table to solve for the constant k. Let's use 40 photos with a cost per photo of 2.5 cents:
2.5 = k/40
k = 2.5 * 40
k = 100
Therefore, the function that models the data is:
c = 100/n