Pepe's pizza makes 52 pizza crusts the first week and 180 pizza crusts each subsequent week. dianne's delicatessen makes 26 pizza crusts the first week and 90 pizza crusts each subsequent week. in how many weeks will the total number of pizza crusts made by pepe's pizza equal twice the total number of pizza crusts made by dianne's delicatessen?

Let pn  = The total number of pizza crusts made by the end of the nth week

For Pepe's Pizza:
Pn + 52 + 180n 

For Diannes's 
Pn = 25 + 90n 

The total number of pizza crusts made by Pep's Pizza equals twice the total number of pizza crusts made by Dianne's Delicatessen when:
52 + 180n = 2 (26 + 90n)
52 + 180n = 52 + 180n 

This equation is satisfied for any value of n, so Pepe's always makes twice as much as Dianne's

Period is the time it takes for one “cycle” to complete. in the parent sine function, period is 2*pi since sin(0) = 0, sin(pi/2) = 1, sin(pi) = 0, sin(3pi/2) = -1, and sin(2pi) = 0. at that point, the sequence repeats itself. i’m not sure if your graph is similar to the sine function since you didn’t provide a picture, but you can find the period by looking at a graph.