Problem Set 1. The costs to purchase school spirit posters are as follows: two posters for $5, four posters for $9, six posters for $13, eight posters for $17, and so on.
a. What type of function would best represent the cost of the total number of posters purchased?
b. What function represents the cost of the total number of posters purchased? How did you know? Justify your reasoning.
c. If you have $40 to spend, write an inequality to find the maximum number of posters you could buy.function models the total number of memberships in this si

a. we have the next set of points (2,5), (4,9), (6,13), (8,17), where x represent the quantity of posters and y represent the cost. Graphing these points we have the image attached. As we can see the function is linear

b. To know the linear function we need to find the slope of the line then:

[tex]m=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}=\dfrac{9-5}{4-2}=\dfrac{4}{2}=2[/tex]

Then the slope of the line is 2. Now using the next expression and one point we could find the equation of the line.

[tex]y-y_{1}=m(x-x_{1})\\y-5=2(x-2)\\y-5=2x-4\\y=2x-4+5\\y=2x+1[/tex]

Then the expression of the function is: y=2x+1

c. we have to find the inequality using the function and finding the number of posters x, then:

[tex]y\leq2x+1\\y-1\leq2x\\\dfrac{y-1}{2}\leq x[/tex]

as we have 40 then:

[tex]\dfrac{40-1}{2}\leq x\\\dfrac{39}{2}\leq x\\19.5\leq x[/tex]

The number of posters have to be an integer then the maximum number of posters with $40 is 19.