precalculus help

Question

The median home value in Massachusetts and California (adjusted for inflation) are shown below:

YearMassachusettsCalifornia
1950	55400	57900
2000	185700	211500

If we assume that the house values are changing linearly,

a) In which state have home values increased at a higher rate?

b) If these trends were to continue, what would be the median home value in Massachusetts in 2010?

$  

c) If we assume the linear trend existed before 1950 and continues after 2000, the two states' median house values will be (or were) equal in what year? (The answer might be absurd)

The year _________

Answer 1

Hi Mark,

Whenever we're asked to find a higher "rate of increase," that always means we're looking for the slope. First step is to extrapolate what points we have... For MA, the points are (1950, 55400) and (2000, 185700). For CA, the points are (1950, 57900) and (2000, 211500).

(a) Massachusetts Rate of Change: (185700 - 55400) / (2000 - 1950) = $2606/year

California rate of change: (211500 - 57900) / (2000 - 1950) = $3072/year

California's home prices increase at a higher rate.

(b)

If we follow a linear trend, let's come up with an equation using x=year and y=median home value. I'm going to use point-slope-form to create my equation; point = (1950, 55400) and slope = 2606

y-55400 = 2606(x-1950)

plugging in x=2010:

y = $211760 in 2010

(c)

To find the year in which median home values are equal, we want to find the intersection point of each trend-line. We found Massachusetts's trend line in part (b); now do the same for California (point: (1950, 57900), slope: 3072)

California: y-57900 = 3072(x-1950)

Massachusetts: y-55400 = 2606(x-1950)

These points intersect at $41419 in 1944.