Question

Since 2003 median home prices in Midvale, UT have been growing exponentially at roughly 4.7 % per year. If you had purchased a house in Midvale, UT for $ 172000 in 2004 in what year would the home be worth $ 249000 ?

Answer 1

Answer:

The home would be worth $249000 during the year of 2012.

Step-by-step explanation:

The price of the home in t years after 2004 can be modeled by the following equation:

$P(t) = P(0)(1+r)^{t}$

In which P(0) is the price of the house in 2004 and r is the growth rate.

Since 2003 median home prices in Midvale, UT have been growing exponentially at roughly 4.7 % per year.

This means that $r = 0.047$

$172000 in 2004

This means that $P(0) = 172000$

What year would the home be worth $ 249000 ?

t years after 2004.

t is found when P(t) = 249000. So

$P(t) = P(0)(1+r)^{t}$

$249000 = 172000(1.047)^{t}$

$(1.047)^{t} = \frac{249000}{172000}$

$\log{(1.047)^{t}} = \log{\frac{249000}{172000}}$

$t\log(1.047) = \log{\frac{249000}{172000}}$

$t = \frac{\log{\frac{249000}{172000}}}{\log(1.047)}$

$t = 8.05$

2004 + 8.05 = 2012

The home would be worth $249000 during the year of 2012.