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?
Let x represent the number of photos bought and y represent the cost per photo.
x | y
--|--
1 | $5
5 | $4
10 | $3.50
20 | $3
50 | $2.50
100 | $2
To find the function that models this data, we can start by finding the relationship between x (number of photos) and y (cost per photo).
We can see that as the number of photos bought increases, the cost per photo decreases. This is an inverse relationship.
The general form of an inverse relationship is y = k/x, where k is a constant. We can find the value of k by plugging in one set of values from the table.
Using x=1 and y=$5, we get:
5 = k/1
k = 5
Therefore, the function that models the data is:
y = 5/x