The number of users on a website is 1500 and is growing exponentially at a rate of 27% per year. Write a function to represent the number of users on the website after tt years, where the monthly 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 month, to the nearest hundredth of a percent.

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slicergiza slicergiza · Answer 1 · 2019-10-10T19:34:26+02:00

Answer:

[tex]A=1500(1+0.27)^t[/tex]

Rate of change per month would be 2.01%

Step-by-step explanation:

Since, the exponential growth function,

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Where,

P = principal amount,

r = annual rate,

n = number of compounding periods,

t = number of years,

Here,

P = 1500, r = 27% = 0.27, n = 1,

Thus, the number of users after t years,

[tex]A=1500(1+0.27)^t[/tex]

Let it is equivalent to number of users when it is growing at the rate of x monthly,

That is,

[tex]1500(1+0.27)^t=1500(1+x)^{12t}[/tex]

[tex]1.27^t=((1+x)^{12})^t[/tex]

By comparing,

[tex](1+x)^{12}=1.27[/tex]

[tex]\implies 1 + x = 1.02012\implies x = 0.02012=2.012\%\approx 2.01\%[/tex]