I'm stuck on what I think should be a relatively simple question. A person has a choice of two jobs. Job A starts at £20000 pa, but increases at a rate of 5% a year. Job B starts at £30000 pa, but increases at 1% a year.
I would like to know after how many years (i.e. for what value of t) the salary of Job A will overtake that of Job B. I've tried to turn it into an inequality as follows, where t is the number of years:
20000 x 1.05^t > 30000 x 1.01^t
My guess is that something needs to be done with logarithms in order to bring t down from being a power. But no matter what I do, I seem to come up with the rather infuriating and obvious conclusion that "202.98t > 43.09t"!
Any help or suggestions as to how I can find the value of t which fulfills the inequality?
Thank you so much for your help in advance. I've been pulling my hair out for a while, and have a feeling I will kick myself when I find out the answer! >_< I've found the answer by trial and error, but would like an exact value for t and some proper mathematical technique if possible.
EDIT: Sorry if this is in the wrong forum. I chose the one I think my dilemma fits into best. Mods, please feel free to shift it around!