if you start from the "standard" sine function, i.e.
you can change its graph in four ways:
amplitude: you can multiply the whole function by a constant to stretch/squeeze it vertically. the transformation looks like
phase: you can add a constant to the argument translate it horizontally. the transformation looks like
period: you can multiply the argument by a constant to stretch/squeeze it horizontally. the transformation looks like
shift: you can add a constant to the whole function to translate it vertically. the transformation looks like
in your case, we're changing the period of the function. if the function is squeezed, so you're squeezing the graph horizontally by a factor of 7/4
subtract 1.88 from each side
8-1.88 = 1.88-1.88+a
6.12 = a
8 = 1.88+a
8 = 1.88+6.12
you would get 50 coins in that time.
to find this, we first need to find the unit rate. we can get that by dividing the amount of coins by the amount of time.
15 coins/ 30 mins = .5 coins per minute.
now, we have 100 minutes in the second part of the problem, so we multiply the rate by that amount of time.
.5 coins per min * 100 mins = 50 coins