SOLUTION: If a piece of real estate purchased for $50,000 in 1998 appreciates at the rate of 5% per year, then its value t years after the purchase will be f (t) = 50,000(1.05t ) . Accordi

Algebra ->  Rational-functions -> SOLUTION: If a piece of real estate purchased for $50,000 in 1998 appreciates at the rate of 5% per year, then its value t years after the purchase will be f (t) = 50,000(1.05t ) . Accordi      Log On


   

Question 107480: If a piece of real estate purchased for $50,000 in 1998 appreciates at
the rate of 5% per year, then its value t years after the purchase will
be f (t) = 50,000(1.05t ) . According to this model, by how much will the
value of this piece of property increase between the years 2007 and
2008?
a. $2500
b. $3140
c. $3880
d. $31,400
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
First, a correction.
If the property appreciates 5% every year, then after the first year,1999.
F(1)=50000(1.05)
After the second year, 2000.
F(2)=F(1)*(1.05)=50000(1.05)(1.05)=50000%281.05%29%5E2
The equation should be
F%28t%29=50000%281.05%29%5Et
then
2007 would be the 9th year and 2008 would be the 10th year.
F%289%29=50000%281.05%29%5E9 and
F%2810%29=50000%281.05%29%5E10
or
F%289%29=77566 and
F%2810%29=81445
The difference between the 10th year and the 9th year would then be
F%2810%29-F%289%29=3879
C.3880, close enough.
If you used the original equation, the house value increases only $2500,
after the first year but then increases value by $52,500 every year after.
At the end of the 10th year, the house would be worth $525,000.
That would be a great profit.