Answer:
(a) Function type
The function of house 1 is exponential
The function of house 2 is linear
(b) Function
--- House 1
--- House 2
(c) House with the greatest value in 30 years:
House 1
Step-by-step explanation:
Given
Solving (a): The type of function
First, we check if the function is linear by calculating the difference between each year
<u>House 1</u>
The difference are not equal; hence, the function is not linear. So, we can assume that it is exponential (the second option)
<u>House 2</u>
The difference are equal; hence, the function is linear.
Solving (b): The function of each
<u>House 1</u>
An exponential function is represented as:
When
We have:
---- (1)
When
We have:
--- (2)
Divide (2) by 1
Make a the subject in (1)
So, the function is:
<u>House 2</u>
A linear function is represented as:
First, we calculate the slope (m)
So, we have:
So, the equation is:
This gives:
So, the function is:
Solving (c): House with the greatest value in 30 years
This means that:
For house 1, we have:
For house 2, we have:
By comparison;
House 1 will have a greater value in 30 years
And the difference between the values is significant
The difference is: