Question

An abandoned building's value is 230(0.95)^t thousand dollars. When will Etienne be able to buy the building with his savings account, which has $150,000 at year t= 0 and is growing by 11% per year?

Answer 1

I just need help setting up the formula, that's all :)

Answer 2

If I read it correctly you want
230000(.95)^t = 150000(1.11)^t

23(.95^t) = 15(1.11)^t
take logs of both sides and use log rules
log 23 + t log .95 = log 15 + t log 1.11
log 23 - log 15 = t(log 1.11 - log .95)


carry on

Answer 3

thank you very much! I understand it now :)

Answer 4

or, you can get all the exponents over a single value:

23(.95^t) = 15(1.11)^t
(.95^t)/(1.11)^t = 15/23
(.95/1.11)^t = 15/23
t log(0.856) = log(0.652)
t = log(0.652)/log(0.856) = 2.751

You can see that Reiny's value will agree, since subtracting logs lets you divide numbers. His will probably be more accurate, since the final rounding error will be deferred until the last step.