Question

Belinda is thinking about buying a house for $249,000. 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) 253,980 259,059.60 264,240.79
House 2 (value in dollars) 256,000 263,000 270,000

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. (2 points)

Part B: Write one function for each house to describe the value of the house f(x), in dollars, after x years. (4 points)

Part C: Belinda wants to purchase a house that would have the greatest value in 45 years. Will there be any significant difference in the value of either house after 45 years? Explain your answer, and show the value of each house after 45 years. (4 points)

Answer 1

The value of House 1 can be described by a linear function, while the value of House 2 can be described by an exponential function. The functions f(x) for each house are f(x) = 249,000 + 6,000x for House 1 and f(x) = 249,000 * 1.05^x for House 2. After 45 years, House 2 will have a significantly higher value than House 1.

Step-by-step explanation:

Part A: To determine if the value of each house is described by a linear or exponential function, we need to analyze the data. A linear function has a constant rate of change, while an exponential function has a constant ratio of change. Looking at the table, we can see that the value of House 1 increases by approximately $6,000 in each year, indicating a linear function. On the other hand, the value of House 2 increases by a constant ratio of approximately 1.05, suggesting an exponential function.

Part B: For House 1, the function f(x) can be written as f(x) = 249,000 + 6,000x, where x is the number of years. For House 2, the function f(x) can be written as f(x) = 249,000 * 1.05^x.

Part C: To determine if there will be a significant difference in the value of either house after 45 years, we can calculate the value of each house after 45 years. For House 1, f(45) = 249,000 + 6,000 * 45 = $519,000. For House 2, f(45) = 249,000 * 1.05^45 = $1,650,694. Therefore, there will be a significant difference in the value of the two houses after 45 years, with House 2 having a much higher value.

Answer 2

This is the answer hope you