Question

The median home sale price in country A has been rising approximately linear since 1995. The median home sale price in 1995 was $120,500. The median home sale price in 2004 was $197,900. Let P be the median home sale price and let t be the number of years since1995.A) determine a function P(t) that fits this data P(t)=part BUse the function from part A to estimate the median home sale price in 2000

Answer 1

Part A

Given:

The rise is approximately linear

Median home sale price in 1995 = $120,500

Median home sale price in 2004 = $197,900

A linear equation is generally represented by the equation:

`\begin{gathered} y\text{ = mx + c} \\ Where\text{ m is the slope and} \\ c\text{ is the intercept} \end{gathered}`

Take 1995 as t = 0

At 2004, t = 9

The slope (m) of the equation can be found using the formula:

`m\text{ =}\frac{P(t=9)\text{ -P\lparen t=0\rparen}}{9-0}`

Substituting the given values:

`\begin{gathered} m\text{ = }\frac{197900\text{ - 120500}}{9-0} \\ =\text{ 8600} \end{gathered}`

The intercept c is value P(t) at t = 0 :

P(t=0) = 120500

Hence, the function that fits the data is:

P(t) = 8600t + 120500

Part B

The median home sale price in 2000 can be obtained by substitution

In year 2000, t = 5:

`\begin{gathered} P(t=5)\text{ = 8600}*\text{5 + 120500} \\ \text{ = 163500} \end{gathered}`

The median home sale in year 2000 is $163500