A woman made $45,000 during the first year of her new job at city hall. Each year she received a 10% raise. Find her total earnings during the first nine years on the job.

Question

A woman made $45,000 during the first year of her new job at city hall. Each year she received a 10% raise. Find her total earnings during the first nine years on the job.

Answer 1

first year she made 45000

after two years she had 45000 + 45000(1.2)
after tree years she had 45000 + 45000(1.1)^2
...

This is a geometric series where
a = 45000
r = 1.1
n = 9

Now use your formula

Answer 2

45k

45(1+.1)
45(1+.1)^2
and so on. Isnt this a geometric series?

Sum a(1+.1)^n where n goes from 0 to 9

http://en.wikipedia.org/wiki/Geometric_series

Answer 3

To find the woman's total earnings during the first nine years on the job, you can calculate the sum of her earnings for each year.

In the first year, she earned $45,000.
In the second year, she received a 10% raise, so her salary increased by 10% of $45,000, which is $4,500. Her salary for the second year would be $45,000 + $4,500 = $49,500.
In the third year, her salary would be increased again by 10% of $49,500, which is $4,950. Her salary for the third year would be $49,500 + $4,950 = $54,450.
You can continue this pattern of calculating the salary for each subsequent year until you reach the ninth year.

Alternatively, you can use a formula to calculate the total earnings. Since the raises are based on a percentage, you can use the formula for the sum of an arithmetic series:

Total earnings = (Initial salary + Final salary) * Number of years / 2

In this case, the initial salary is $45,000, the final salary is the salary in the ninth year (calculated using the raise pattern), and the number of years is 9.

Let's calculate the total earnings.