Question

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.​

Answer 1

Answer:

The expression that models the growth of users is: $users(t) = 5400*1.3^t$

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:

$users(1) = 5400*1.3$

After the second year we will have:

$users(2) = users(1)*1.3\\users(2) = 5400*1.3*1.3 = 5400*(1.3)^2$

After the third year we will have:

$users(3) = users(2)*1.3\\users(3) = 5400*(1.3)^2*1.3 = 5400*(1.3)^3$

This will continue as the years passes. Therefore:

$users(t) = 5400*1.3^t$

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

$\text{rate per quarter} = \frac{30}{4} = 7.5\%$