Question

Home Prices The median selling price of an existing home in the United States increased continuously over the period 2011–2013 at the rate of 8.5% per year from approximately $166,000 in 2011.27 Write down a formula that predicts the median selling price of an existing home t years after 2011. Use your model to estimate, to the nearest $1,000, the median selling price of an existing home in 2013 and 2015

Answer 1

166,000(1 + 0.085)^t ; $195,000 ; $230,000

Explanation:

Given that :

Rate of increase = 8.5% = 0.085 per year

Initial value ; price in 2011 (A) = $166,000

Formula to predict the median price t years after 2011 ;

At a continous rate :

Median price, P:

P = initial price (1 + rate)^t

P = 166,000(1 + 0.085)^t

t = time since 2011 ;

Median price of home in 2013:

t = 2013 - 2011 = 2

P = 166,000(1 + 0.085)^2

P = 166000(1.085)^2

P = 166000(1.177225)

P = 195419.35

P = $195,000 ( nearest $1000)

Median price of home in 2013:

t = 2015 - 2011 = 4

P = 166,000(1 + 0.085)^4

P = 166000(1.085)^4

P = 166000(1.385858700625)

P = 230052.54430375

P = $230,000 ( nearest $1000)