Question

question 7, 9.c.47 part 1 of 2
in 2000, the median home price in a certain city was about $310,000, and from 2000 to 2006, home prices in this city rose at an average rate of about 10.3% per year. if prices had continued to rise at that rate, what would the median home price have been in 2020? compare this amount to the actual median price of about $400,000 in 2020.
the median home price would be approximately $ million in 2020. (round to two decimal places as needed.)

Explanation:

Step1: Determine the number of years

The time from 2000 to 2020 is $t = 20$ years. The initial price $P_0=\$310000$, and the growth - rate $r = 0.103$.

Step2: Use the compound - growth formula

The compound - growth formula is $P = P_0(1 + r)^t$. Substitute $P_0 = 310000$, $r=0.103$, and $t = 20$ into the formula: $P=310000\times(1 + 0.103)^{20}$.

Step3: Calculate $(1 + 0.103)^{20}$

$(1 + 0.103)^{20}=1.103^{20}\approx7.1066$.

Step4: Calculate the final price

$P = 310000\times7.1066=\$2203046\approx2.20$ million.

Answer:

$2.20$