The red bus company charges $150 plus 72 per hour to rent a bus the blue bus company charges $240 plus 54 per hour for what number of hours with the company charge the same and what will the the charge be for that number of hours

Let's start off by writing equations for each
Let's say the Red Bus Company is Company Red, and the Blue Bus Company is Company Blue to keep it short.
Company Red = 150 + 72(h) whereas h stands for how many hours
Company Blue = 240 + 54(h) whereas h stands for how many hours
Now, we plug in some numbers starting from 1 to see when the companies will match, however, I'll only do 2 examples to keep this short.
Let's start off at 5 hours (you can start off at any, but I prefer to be in the middle to see whether which company surpasses the other in cost and we can build off from there
Company Red:
150 + 72(5)
72 * 5 = 360
150 + 360 = 510
Company Blue:
240 + 54(5)
53 * 5 = 270
240 + 270 = 510
Wow, actually it looks like they charge will be the same after 5 hours. No need to do a second equation since we got it on our first try.

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.