Evelyn took a job that paid $100 the first week. She was guaranteed a raise of 2% each week. How much money will she make in all
1 answer:
This is a growth exponential equation.
It can be solved 2 ways, but one of them is long and cumbersome and not worth the effort. You could take 2% of the base number and keep doing it 8 times.
The other way is to realize that 100$ + 2% of 100 dollars can be written as 2% = 2/100 = 0.02 and that can be written as
100( 1 + 0.02 ) = 100(1.02) Now if you want this to be raised 8 times, it will look like this
y = 100(1.02)^(n - 1) for any number of weeks
y(8) = 100(1.02)^7 = 114.87
So at week 1 she has 100 dollars and at week 8 she has 114.87 dollars.
Comment
Realize that if her boss does not want to give her compounded interest that she could still make
Ln = L
= 100 + (n - 1)*0.02*100
L
= 100 + 7*0.02*100 = 100 + 14. = 114
By compounding she makes a whole 0.87$ more.
It can be solved 2 ways, but one of them is long and cumbersome and not worth the effort. You could take 2% of the base number and keep doing it 8 times.
The other way is to realize that 100$ + 2% of 100 dollars can be written as 2% = 2/100 = 0.02 and that can be written as
100( 1 + 0.02 ) = 100(1.02) Now if you want this to be raised 8 times, it will look like this
y = 100(1.02)^(n - 1) for any number of weeks
y(8) = 100(1.02)^7 = 114.87
So at week 1 she has 100 dollars and at week 8 she has 114.87 dollars.
Comment
Realize that if her boss does not want to give her compounded interest that she could still make
Ln = L
L
By compounding she makes a whole 0.87$ more.
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