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

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

19

step-by-step explanation: