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:
[tex]\begin{gathered} y\text{ = mx + c} \\ Where\text{ m is the slope and} \\ c\text{ is the intercept} \end{gathered}[/tex]Take 1995 as t = 0
At 2004, t = 9
The slope (m) of the equation can be found using the formula:
[tex]m\text{ =}\frac{P(t=9)\text{ -P\lparen t=0\rparen}}{9-0}[/tex]Substituting the given values:
[tex]\begin{gathered} m\text{ = }\frac{197900\text{ - 120500}}{9-0} \\ =\text{ 8600} \end{gathered}[/tex]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:
[tex]\begin{gathered} P(t=5)\text{ = 8600}\times\text{5 + 120500} \\ \text{ = 163500} \end{gathered}[/tex]The median home sale in year 2000 is $163500
