Belinda is thinking about buying a house for $286,000. 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) 294,580 303,417.40 312,519.92
House 2 (value in dollars) 295,000 304,000 313,000

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 25 years. Will there be any significant difference in the value of either house after 25 years? Explain your answer, and show the value of each house after 25 years. (4 points)

Question

Belinda is thinking about buying a house for $286,000. 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)	294,580	303,417.40	312,519.92
House 2 (value in dollars)	295,000	304,000	313,000

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 25 years. Will there be any significant difference in the value of either house after 25 years? Explain your answer, and show the value of each house after 25 years. (4 points)

Naciama · Answer

Plz I need help with this question. Im doing a test right now

mhanifa · Answer

Compare the prices, if the differences are same, it is linear. If the ratios are same, it is exponential.

Naciama · Answer

I don't really understand part B. Can I plz get the answer for that

mhanifa · Answer

$$f(x) = P*r ^{x}$$
this is form of the exponential function, where P- initial value, r- common ratio

Naciama · Answer

How do I plug in the numbers. 
sry my teacher isn't rlly good at explaining

mhanifa · Answer

$$f(x) = P - dx$$
this is the form of the linear function, where P- initial price and d- common ratio

Naciama · Answer

What is the common ratio?

mhanifa · Answer

P is the value at year 1

mhanifa · Answer

Common ratio is the number you get when divide the prices and you get same number for both.

mhanifa · Answer

Common difference is the number you get when subtract the prices and you get same number.

mhanifa · Answer

From the first look, the house 1 is exponential and house 2 is linear.

Naciama · Answer

I agree. can I get the answer to the question though. Because this test is timed and I only have 4 min left

mhanifa · Answer

To find r you need r = 312,519.92/303,417.40

mhanifa · Answer

To find d you need d = 313,000 - 304,000

Naciama · Answer

ohhh thank you. what about the X exponent for house 1

mhanifa · Answer

x stays as is

mhanifa · Answer

For the second one you need:
$$f(x) = P + dx$$

mhanifa · Answer

Not as I gave above

Naciama · Answer

wait is that for house 2?

mhanifa · Answer

Yes

Naciama · Answer

okay I appreciate it

mhanifa · Answer

For Part C, you need to substitute x with 25 in both equations and compare the values

Naciama · Answer

ohhh ok

mhanifa · Answer

I have to leave, good luck. Hope you can complete it

Naciama · Answer

ok last question. so I would add the two last values for d house 2

mhanifa · Answer

$$f(x) = 295000 + 9000x$$

Naciama · Answer

thanks

mhanifa · Answer

NP, sorry I have to leave.

Naciama · Answer

ok