If you earn $3200 per month and you expect your earnings to increase by 6.4% per year, how much do you think you will be making in 6 years?

You should expect to be making $55,716.14 in 6 years.

Step-by-step explanation:

Your earnings after t years is given by the following equation:

In which E(0) is how much you earn on the current year and r is the increase rate, as a decimal.

$3200 per month currently:

A year has 12 months. So

You expect your earnings to increase by 6.4% per year

So

Then

How much do you think you will be making in 6 years?

This is E(6).

You should expect to be making $55,716.14 in 6 years.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for