Kwan's parents bought a home for $50,000 in 1997 just as real estate values in the area started to rise quickly. each year, their house was worth more until they sold the home for $309,587. model the growth of the home's value from 1997 to 2007 with both linear and an exponential equation. graph the two models below.

A. First let us start with the linear model.

The equation is in the form of y = m x + b

Calculating for the slope m:

m = (309,587 – 50,000) / (2007 – 1997)

m = 25,958.7

Subsituting:

y = 25,958.7 x + b

Taking x = 1997, y = 50,000. Solve for b:

50,000 = 25,958.7 (1997) + b

b = -51,789,523.9

The complete equation is therefore:

y = 25,958.7 x - 51,789,523.9

B. The exponential model has the following form:

y = a b^x

where a and b are constants

Taking x1= 1997, y1 = 50,000; x2 = 2007, y2 = 309,587

50,000 = a b^1997

309,587 = a b^2007

Combining in terms of a:

50,000 / b^1997 = 309,587 / b^2007

b^2007 / b^1997 = 309,587 / 50,000

b^10 = 6.19174

b = 1.2

Substituting:

y = a 1.2^x

Solving for a:

50,000 = a 1.2^1997

a = 3.75 x 10^-154

The complete equation is:

y = 3.75 x 10^-154 * 1.2^x

2x^2+5x+17

your welcome. : )

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."