Question

PLease help

Answer 1

Answer:

(a) Function type

The function of house 1 is exponential

The function of house 2 is linear

(b) Function

$f(x) = 179000 * 1.04^x$ --- House 1

$f(x) =11000x+179000$ --- House 2

(c) House with the greatest value in 30 years:

House 1

Step-by-step explanation:

Given

$\begin{array}{cccc}{Years} & {1} & {2} & {3} & {House\ 1} & {186,160 } & {193,606.40 } & {201,350.66} & {House\ 2} & {190,000 } & {201,000 } & {212,000} \ \end{array}$

Solving (a): The type of function

First, we check if the function is linear by calculating the difference between each year

House 1

$d = 193606.40 - 186160 = 7446.4$

$d = 201350.66 - 193606.40 = 7744.26$

The difference are not equal; hence, the function is not linear. So, we can assume that it is exponential (the second option)

House 2

$d = 201000 - 190000 =11000$

$d = 212000 - 201000 =11000$

The difference are equal; hence, the function is linear.

Solving (b): The function of each

House 1

An exponential function is represented as:

$y = ab^x$

When $x = 1;\ y =186,160$

We have:

$186,160 =ab^1$

$186,160 =ab$ ---- (1)

When $x = 2;\ y =193606.40$

We have:

$193606.40 =ab^2$ --- (2)

Divide (2) by 1

$\frac{193606.40}{186160} =\frac{ab^2}{ab}$

$1.04 = b$

$b = 1.04$

Make a the subject in (1)

$186,160 =ab$

$a = \frac{186160}{b}$

$a = \frac{186160}{1.04}$

$a = 179000$

So, the function is:

$f(x) = 179000 * 1.04^x$

House 2

A linear function is represented as:

$y = mx + b$

First, we calculate the slope (m)

$m = \frac{y_2 -y_1}{x_2 - x_1}$

So, we have:

$m = \frac{201000 - 190000}{2 - 1}$

$m = \frac{11000}{1}$

$m = 11000$

So, the equation is:

$y =m(x-x_1) + y_1$

This gives:

$y =11000(x-1) + 190000$

$y =11000x-11000 + 190000$

$y =11000x+179000$

So, the function is:

$f(x) =11000x+179000$

Solving (c): House with the greatest value in 30 years

This means that:

$x = 30$

For house 1, we have:

$f(x) = 179000 * 1.04^x$

$f(30) = 179000 * 1.04^{30}$

$f(30) = 580568.15$

For house 2, we have:

$f(x) =11000x+179000$

$f(30) = 11000 * 30+ 179000$

$f(30) = 509000$

By comparison;

$580568.15> 509000$

House 1 will have a greater value in 30 years

And the difference between the values is significant

The difference is:

$d =580568.15-509000$

$d =71568.15$