You have an initial amount of $45 in a savings account and you deposit an equal amount into the account each week. after 5 weeks the account holds $105. write an equation that represents the amount y (in dollars) of money in the account after x weeks.

Given:
initial deposit = 45
total deposit = 105
w = weekly deposit
x = no. of weeks = 5 weeks
y = amount in dollars

45 + 5w = 105
45 + 5w = 105
5w  = 105 - 45
5w =  60
w = 60/5
w = $12 weekly deposit.

y = $45 + $12x  

x = (y - 45)/12

To check:
y = 45 + 12(5)
y = 45 + 60
y = 105 total deposit in 5 weeks

x = (105-45)/12
x = 60/12
x = 5 weeks

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.