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
![\begin{array}{cccc}{Years} & {1} & {2} & {3} & {House\ 1} & {186,160 } & {193,606.40 } & {201,350.66} & {House\ 2} & {190,000 } & {201,000 } & {212,000} \ \end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bcccc%7D%7BYears%7D%20%26%20%7B1%7D%20%26%20%7B2%7D%20%26%20%7B3%7D%20%20%26%20%7BHouse%5C%201%7D%20%26%20%7B186%2C160%20%7D%20%26%20%7B193%2C606.40%20%7D%20%26%20%7B201%2C350.66%7D%20%26%20%20%7BHouse%5C%202%7D%20%26%20%7B190%2C000%20%7D%20%26%20%7B201%2C000%20%7D%20%26%20%7B212%2C000%7D%20%5C%20%5Cend%7Barray%7D)
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>
![d = 201350.66 - 193606.40 = 7744.26](https://tex.z-dn.net/?f=d%20%3D%20201350.66%20-%20%20193606.40%20%3D%207744.26)
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>
![d = 201000 - 190000 =11000](https://tex.z-dn.net/?f=d%20%3D%20201000%20-%20190000%20%3D11000)
![d = 212000 - 201000 =11000](https://tex.z-dn.net/?f=d%20%3D%20212000%20-%20201000%20%3D11000)
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:
![y = ab^x](https://tex.z-dn.net/?f=y%20%3D%20ab%5Ex)
When ![x = 1;\ y =186,160](https://tex.z-dn.net/?f=x%20%3D%201%3B%5C%20y%20%3D186%2C160)
We have:
![186,160 =ab^1](https://tex.z-dn.net/?f=186%2C160%20%3Dab%5E1)
---- (1)
When ![x = 2;\ y =193606.40](https://tex.z-dn.net/?f=x%20%3D%202%3B%5C%20y%20%3D193606.40)
We have:
--- (2)
Divide (2) by 1
![\frac{193606.40}{186160} =\frac{ab^2}{ab}](https://tex.z-dn.net/?f=%5Cfrac%7B193606.40%7D%7B186160%7D%20%3D%5Cfrac%7Bab%5E2%7D%7Bab%7D)
![1.04 = b](https://tex.z-dn.net/?f=1.04%20%3D%20b)
![b = 1.04](https://tex.z-dn.net/?f=b%20%3D%201.04)
Make a the subject in (1)
![186,160 =ab](https://tex.z-dn.net/?f=186%2C160%20%3Dab)
![a = \frac{186160}{b}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7B186160%7D%7Bb%7D)
![a = \frac{186160}{1.04}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7B186160%7D%7B1.04%7D)
![a = 179000](https://tex.z-dn.net/?f=a%20%3D%20179000)
So, the function is:
![f(x) = 179000 * 1.04^x](https://tex.z-dn.net/?f=f%28x%29%20%3D%20179000%20%2A%201.04%5Ex)
<u>House 2</u>
A linear function is represented as:
![y = mx + b](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20b)
First, we calculate the slope (m)
![m = \frac{y_2 -y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_2%20-y_1%7D%7Bx_2%20-%20x_1%7D)
So, we have:
![m = \frac{201000 - 190000}{2 - 1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B201000%20-%20190000%7D%7B2%20-%201%7D)
![m = \frac{11000}{1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B11000%7D%7B1%7D)
![m = 11000](https://tex.z-dn.net/?f=m%20%3D%2011000)
So, the equation is:
![y =m(x-x_1) + y_1](https://tex.z-dn.net/?f=y%20%3Dm%28x-x_1%29%20%2B%20y_1)
This gives:
![y =11000(x-1) + 190000](https://tex.z-dn.net/?f=y%20%3D11000%28x-1%29%20%2B%20190000)
![y =11000x-11000 + 190000](https://tex.z-dn.net/?f=y%20%3D11000x-11000%20%2B%20190000)
![y =11000x+179000](https://tex.z-dn.net/?f=y%20%3D11000x%2B179000)
So, the function is:
Solving (c): House with the greatest value in 30 years
This means that:
![x = 30](https://tex.z-dn.net/?f=x%20%3D%2030)
For house 1, we have:
![f(x) = 179000 * 1.04^x](https://tex.z-dn.net/?f=f%28x%29%20%3D%20179000%20%2A%201.04%5Ex)
![f(30) = 179000 * 1.04^{30}](https://tex.z-dn.net/?f=f%2830%29%20%3D%20179000%20%2A%201.04%5E%7B30%7D)
![f(30) = 580568.15](https://tex.z-dn.net/?f=f%2830%29%20%3D%20580568.15)
For house 2, we have:
![f(x) =11000x+179000](https://tex.z-dn.net/?f=f%28x%29%20%3D11000x%2B179000)
![f(30) = 11000 * 30+ 179000](https://tex.z-dn.net/?f=f%2830%29%20%3D%2011000%20%2A%2030%2B%20179000)
![f(30) = 509000](https://tex.z-dn.net/?f=f%2830%29%20%3D%20509000)
By comparison;
![580568.15> 509000](https://tex.z-dn.net/?f=580568.15%3E%20509000)
House 1 will have a greater value in 30 years
And the difference between the values is significant
The difference is:
![d =580568.15-509000](https://tex.z-dn.net/?f=d%20%3D580568.15-509000)
![d =71568.15](https://tex.z-dn.net/?f=d%20%3D71568.15)
Answer:
It is an unknown number but add 16 + 32 degrees and you get 48x degrees then multiply 48 X 72 degrees and you get 336 degrees.
Step-by-step explanation:
Answer:
$5,500 per a year
Step-by-step explanation:
there are 3 years in between 2009 and 2012, and the is a difference of $16,500 between the two years so $16,500/3= $5,500 per 1 year
Find the intersection and probably you will find your answer
Perimeter of hexagon
P = 6x
so answer
B. 6x