The number of users on a website is 5400 and is growing exponentially at a rate of 30% per year. Write a function to represent the number of users on the website after t
years, where the quarterly rate of change can be found from a constant in the
function. Round all coefficients in the function to four decimal places. Also,
determine the percentage rate of change per quarter, to the nearest hundredth of a
percent.

The expression that models the growth of users is:

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:

After the second year we will have:

After the third year we will have:

This will continue as the years passes. Therefore:

The rate of change pre quarter of year is the rate of change pre year divided by 4,therefore:

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!

what i would say the best answer is a. 40.5