Question

David starts off at a salary of $10,000 per yer. At the end of each year, he will earn a 4% raise on his previous salary. What will be the first year that he makes $15,000? If Valerie starts off at a salary of $10,000 per year and receives an option of a constant raise of $500 then how many years until she first makes $15,000?

Could somebody walk me through on how to do this?

Answer 1

10,000(1.04)^n = 15000
1.04^n = 1.5
take logs of both sides

log 1.04^n = log 1.5
n log 1.04 = log 1.5
n = log 1.5/log1.04 = 10.338..
10 years will not be enough , so she makes 15,000 or more in the 11 th year

for the second question you have an arithmetic sequence with
a = 10000
d = 500
n = ?

a + (n-1)d = 15000
10000 + 500(n-1) = 15000
500(n-1) = 5000
n-1 = 10
n = 11