SOLUTION: Susan purchased a painting in the year 2000 for $5000. Assuming an exponential rate of inflation of 3.5% per year, how much will the painting be worth 6 years later?

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Susan purchased a painting in the year 2000 for $5000. Assuming an exponential rate of inflation of 3.5% per year, how much will the painting be worth 6 years later?       Log On


   



Question 1115872: Susan purchased a painting in the year 2000 for $5000. Assuming an exponential rate of inflation of 3.5% per year, how much will the painting be worth 6 years later?

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
%22%245000%22%2A1.035%5E6=%22%246146%22 (rounded)
Each year, the inflation-adjusted value would be
103.5%25%22=103.5%2F100=1.035 the value from the year before.
In math class, we worship the irrational number e ,
so we like to express exponentials in terms of e .
1.035%5E6=e%5Eln%281.035%5E6%29=e%5E6%2Aln%281.035%29 ,
so we could say the value after 6 years is
%22%245000%22%2Ae%5E%28ln%281.035%29%2A6%29 ,
and after t years it would be
%22%245000%22%2Ae%5E%28ln%281.035%29%2At%29 .