Question

Even though housing prices have been declining in many parts of the country, in Lara's neighborhood, they have been increasing steadily since Lara bought her home in 2006. Lara purchased her home in 2006 for $120,000 and it steadily increased its value by $3900 a year. Let V represent the market value (in dollars) of her home; x, the length of time she has lived there (in years). Complete parts a through d below.a.) complete the table b.) write a symbolic rule that expresses v in terms of x. c.) determine the expected value of her home in 2016. d.) in which year is the value of her home expected to reach $174,600

Answer 1

a)

Let's complete the table, first.

x is the number of values she has lived.

V is the value of the house.

From 2006 to 2011 is 5 years, that is an increase of 3900(5) = 19,500

So, the value of the hosue was 120,000 + 19,500 = 139,500

From 2011 to 2014 is 3 years, that is an increase of 3900(3) = 11,700

So, the value of the house was 139,500 + 11,700 = 151,200

Now, we can complete the table, shown below:

Year x V

2006 0 $120,000

2011 5 $139,500

2014 8 $151,200

b)

V is basically 120,000 (initial value) PLUS 3900 for each year, x.

So, we can express this as:

`V=120000+3900x`

c)

Now, we have the equation. We can plug in x (the number of years lived since 2006) and find the market value at any year.

We need expected value in 2016.

That is 10 years from 2006. So, x = 10.

The value would be:

`\begin{gathered} V=120000+3900x \\ V=120000+3900(10) \\ V=\$159,000 \end{gathered}`

The value would be $159,000

d)

We now have V = 174,600. We need to solve for x first.

`\begin{gathered} V=120000+3900x \\ 174,600=120,000+3900x \\ 54,600=3900x \\ x=(54600)/(3900) \\ x=14 \end{gathered}`

This means 14 years from 2006.

That would be:

2006 + 14 = 2020

The year 2020, the expected value of her home would be $174,600