Answer:
The expression that models the growth of users is: ![users(t) = 5400*1.3^t](https://tex.z-dn.net/?f=users%28t%29%20%3D%205400%2A1.3%5Et)
The rate of change per quarter is 7.5%
Step-by-step explanation:
Since the number of users is growing at a rate of 30% per year, then initially we have 5400, but after the first year we will have:
![users(1) = 5400*1.3](https://tex.z-dn.net/?f=users%281%29%20%3D%205400%2A1.3)
After the second year we will have:
![users(2) = users(1)*1.3\\users(2) = 5400*1.3*1.3 = 5400*(1.3)^2](https://tex.z-dn.net/?f=users%282%29%20%3D%20users%281%29%2A1.3%5C%5Cusers%282%29%20%3D%205400%2A1.3%2A1.3%20%3D%205400%2A%281.3%29%5E2)
After the third year we will have:
![users(3) = users(2)*1.3\\users(3) = 5400*(1.3)^2*1.3 = 5400*(1.3)^3](https://tex.z-dn.net/?f=users%283%29%20%3D%20users%282%29%2A1.3%5C%5Cusers%283%29%20%3D%205400%2A%281.3%29%5E2%2A1.3%20%3D%205400%2A%281.3%29%5E3)
This will continue as the years passes. Therefore:
![users(t) = 5400*1.3^t](https://tex.z-dn.net/?f=users%28t%29%20%3D%205400%2A1.3%5Et)
The rate of change pre quarter of year is the rate of change pre year divided by 4,therefore:
![\text{rate per quarter} = \frac{30}{4} = 7.5\%](https://tex.z-dn.net/?f=%5Ctext%7Brate%20per%20quarter%7D%20%3D%20%5Cfrac%7B30%7D%7B4%7D%20%3D%207.5%5C%25)