Question

Jorge is offered two different jobs. One pays a starting salary of $50000 per year, with a guaranteed raise of $1000 every year. The other job pays a starting salary of $25000 per year with a 5% increase in pay every year. a) how long would Jorge/George/Gorge have to work before the two jobs paid the same salary?
So far, I've modeled the salary of the two jobs as following: Job 1: A(t) = 50000 + 1000t, Job 2: A(t) = 25000(1.05)^t. The answer is approximately t = 21.5 and the only method that i know of is comparing the graphs of the two functions and guessing the answer.

Answer 1

I'd like to know if there is a way to solve this problem algebraically.

Answer 2

After working through it a little bit i get:
\[50000t + 1000t = 25000(1.05)^t \]
\[2 + t/25 = 1.05^t\]
\[\log(2+t/25) = tlog(1.05)\]
\[t = (\log(2+t/25))/(\log(1.05))\]

Answer 3

I'd say...Make a table and keep going until you get two matching answers.

I got a Math Ph.D so definitely I'm right.

Answer 4

That's what i wanted to avoid doing. Thanks for your input but i was just wondering if there is some way to solve it algebraically.

Answer 5

Hmm Try finding someone else's help. Unfortunately I could not find the answer when I googled it.

Answer 6

It's alright i found out that there is no algebraic solution.

Answer 7

50,000 ( 1.02) ^t = 25,000 ( 1.05 ) ^t
2 ( 1.02) ^t = ( 1.05 ) ^t