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 I the table below. What function models the data?

Answer 1

To determine the function that models the data, we need to analyze the relationship between the cost per photo and the number of photos bought.

Let's observe the given data:

Number of Photos (x)       Cost per Photo (y)
1              100
10            50
25            40
50            20
100           10

From the table, we can see that as the number of photos bought increases, the cost per photo decreases.

To model this inversely proportional relationship, we can use the equation:

y = k/x

where y represents the cost per photo, x represents the number of photos bought, and k is the constant of variation.

To find the value of k, we can use any of the given data points:

Using the data for 10 photos at a cost per photo of 50, we can substitute x=10 and y=50 into the equation:

50 = k/10
50 * 10 = k
k = 500

Now we know that the equation is:

y = 500/x

Thus, the function that models the data is:

f(x) = 500/x