Question

2) A $100,000 house appreciates at a rate of $3500 a year.
a. Find the equation that models the value of the house in y dollars after x years.
b. Find the value of the house in 12 years.
c. How many years from now will the value of the house be $124,500?

Answer 1

Answer:

Part a) $y=3,500x+100,000$

Part b) $\ 142,000$

Part c) $7\ years$

Step-by-step explanation:

Part a) Find the equation that models the value of the house in y dollars after x years

we know that

The linear equation in slope intercept form is equal to

$y=mx+b$

where

m is the rate or slope

b is the y-coordinate of the y-intercept (initial value)

Let

x -----> the number of years

y ----> the value of the house in dollars

In this problem we have

$m=3,500\ \frac{\ }{year}$

$b=\ 100,000$

substitute

$y=3,500x+100,000$

Part b) Find the value of the house in 12 years.

so

For x=12 years

substitute in the equation and solve for y

$y=3,500(12)+100,000$

$y=\ 142,000$

Part c) How many years from now will the value of the house be $124,500?

For y=$124,500

substitute in the equation and solve for x

$124,500=3,500x+100,000$

subtract 100,000 both sides

$124,500-100,000=3,500x$

$24,500=3,500x$

Divide by 3,500 both sides

$x=7\ years$