Billy earns $25,000 the first year and gets a 5% raise each year. Write a possible explicit rule to describe its pattern. How much will he earn per year after 5 years? 10 years?

Question

anonymous · Answer

@mathstudent55

mathstudent55 · Answer

He earns $25,000. 
That means $25,000 is 100% of his salary, right?

anonymous · Answer

Well that is his starting salary the first year

mathstudent55 · Answer

If he gets a 5% raise, the first year of the raise he will receive 105% of his salary.

anonymous · Answer

5% of 25000 is equal to 1250

anonymous · Answer

but yes $25,000 is 100% of his starting salary the first year

mathstudent55 · Answer

105% = 1.05

anonymous · Answer

1250 * 5 years

anonymous · Answer

and then add to 25000

anonymous · Answer

Y'all are confusing me

anonymous · Answer

@yahya90 I multiply 1250 by 5 then add 25000 to get my answer?

mathstudent55 · Answer

Year         Salary
1              25,000
2              1.05 * 25,000
3              1.05 * (1.05 * 25,000)
4              1.05 * [1.05(1.05 * 25,000)]
5              1.05 * {1.05 * [1.05 * (1.05 * 25,000)]}

anonymous · Answer

yes for 5 years >>>for ten years 10*1250 and then add to 25000

mathstudent55 · Answer

Since each year he gets a 5% raise over the previous year's salary, every year you multiply the previous year's salary by 1.05.

anonymous · Answer

Great thanks you two

anonymous · Answer

Adios

mathstudent55 · Answer

No, wait. @yahya90 is wrong.

anonymous · Answer

Smashing! What is the correct answer then mate?

mathstudent55 · Answer

At the fifth year the pattern is:

5              1.05 * {1.05 * [1.05 * (1.05 * 25,000)]}

Salary $= 1.05^4 * 25,000$

For year n, 

Salary $= 1.05^{n - 1} * 25,000$

For each year you need to figure his salary, multiply 1.05 raised to one less than the year and multiply by 25,000.

anonymous · Answer

5% is 1250 for the first year only >>>it will change in the second year >>>may be

mathstudent55 · Answer

@yahya90 You are solving this as a simple interest type of problem.
The way you are treating this is that he gets 5% of his original 25,000 as a raise each year.

This is a compund interest type problem.
The first year of his raise, he gets 5% of 25,000 = $26,250.
The secnd year of the raise, he gets 5% 0f $26,250 added, not 5% of the original $25,000.
etc.

anonymous · Answer

yes you are right >>>thank you

mathstudent55 · Answer

wlcm