Question

Angelique is thinking about buying a house for $ 179,000 . The table below shows the projected value of two different houses for three years .

Number of years: 1, 2, 3
House 1 ( value in dollars ) : 186,160 ; 193,606.40 ; 201,350.66
House 2 ( value in dollars ) 190,000 ; 201,000 ; 212,000

Part A : What type of function , linear or exponential , can be used to describe the value of each of the houses after a fixed number of years ? Explain your answer .
Part B : Write one function for each house to describe the value of the house f ( x ) , in dollars , after x years .
Part C : Angelique wants to purchase a house that would have the greatest value in 30 years . Will there be any significant difference in the value of either house after 30 years ? Explain your answer , and show the value of each house after 30 years .

Answer 1

House 1 follows an exponential function, House 2 follows a linear function, and the value of each after 30 years can be calculated using their respective formulas.

Step-by-step explanation:

Part A:

The value of House 1 increases by a different amount each year, indicating that it is an exponential function. The value of House 2 increases by the same amount each year, indicating that it is a linear function.

Part B:

House 1: f(x) = 179,000 * (1 + r)^x

House 2: f(x) = 179,000 + r * x

(Note: 'x' represents the number of years and 'r' represents the growth rate/amount per year)

Part C:

After 30 years, the value of House 1 can be calculated using the exponential function:

f(30) = 179,000 * (1 + r)^30

The value of House 2 can be calculated using the linear function:

f(30) = 179,000 + r * 30

To determine if there is a significant difference, you can compare the values obtained for both houses.