Question

A website recorded the numbery of referrals it received from social media websitesover a 10-year period. The results can be modeled byy = 2500(1.50)', where t is the year and O S + < 9.Interpret the values of a and b in this situation. Whatis the annual percent increase? Explain.

Answer 1

Exponential Growth Model

The function that models an exponential growth of some variable is:

`y=a\cdot b^t`

Where a is the initial amount of the variable and b is the base of the exponential function: b = 1 + r and r is the growth rate. We can express the model as:

`y=a\cdot(1+r)^t`

We are given the model as:

`y=2500\cdot(1.50)^t`

We can get the values of a and b by comparing them with the general model:

a = 2500, b = 1.50

We can also find r by solving 1 + r = 1.50 => r = 0.50 = 50%

These values can be interpreted as follows:

There were initially 2500 referrals for the website. It increases by a factor of 1.5 every year, which means the annual percent increase is 50%,