Ask Question
12 June, 21:27

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.

+1
Answers (1)
  1. 12 June, 23:52
    0
    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
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “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 ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers