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?
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
To determine the function that models the data, we need to analyze the relationship between the number of photos and the cost per photo. Based on the given information, we can see that the cost per photo varies inversely with the number of photos.
In an inverse variation, the relationship between two variables can be represented using the equation: y = k/x, where y is the dependent variable, x is the independent variable, and k is the constant of variation.
In this case, y represents the cost per photo and x represents the number of photos. Therefore, we can rewrite the equation as the cost per photo = k/number of photos.
To find the value of k, we will use the information from the table. In an inverse variation, when one variable doubles, the other is halved. Looking at the table, we can see that when the number of photos doubles, the cost per photo is halved.
Using the data from the table, we can find the value of k:
when x = 10, y = $40.
40 = k/10
k = 400.
So the equation representing the data is y = 400/x or the cost per photo = 400/number of photos.