1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
natka813 [3]
3 years ago
10

PLease help

Mathematics
1 answer:
Tom [10]3 years ago
3 0

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

<u>House 1</u>

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)

<u>House 2</u>

d = 201000 - 190000 =11000

d = 212000 - 201000 =11000

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

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

<u>House 2</u>

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

You might be interested in
The Rachel’s daily expenses for 10 days are in the table.
Annette [7]
The correct answer is $44.20. 
If we add up all the tips, the total is $442. If we divide this by the number of days (10), then we find the mean.
442 / 10 = 44.2
4 0
4 years ago
Help with this please!
slega [8]

Hello,

No, this is NOT a proportional relationship.

Have a great day/night and stay safe! :)

8 0
3 years ago
Read 2 more answers
What isthe answer to 3/5 ❌ 20
finlep [7]
3/5 × 20/1 = 12 because 3×20 is 60 and 5×1 is 5 so 60/5 and that simplifies to 12
4 0
3 years ago
Use the following table for questions 11-13.A baseball manager believes a linear relationship exists between the number of Home
slamgirl [31]

The regression equation of Y on X is given by the following formula:

Y-\bar{Y}=b_{yx}(X-\bar{X})

Where byx is given by the formula:

b_{yx}=\frac{N\sum^{}_{}XY-\sum^{}_{}X\sum^{}_{}Y}{N\sum^{}_{}X^2-(\sum^{}_{}X)^2}

Where N is the number of values (N=8). We need to find the sum of X values, the sum of Y values, the average of X, the average of Y, the sum of X*Y and the sum of X^2.

The table of values is:

The values we need to know are on the following table:

By replacing the known values in the formula we obtain:

\begin{gathered} b_{yx}=\frac{8\cdot26125-167\cdot995}{8\cdot4649-(167)^2} \\ b_{yx}=\frac{209000-166165}{37192-27889} \\ b_{yx}=\frac{42835}{9303} \\ b_{yx}=4.6 \end{gathered}

Now, the average of X and Y is the sum divided by N, then:

\begin{gathered} \bar{X}=\frac{167}{8}=20.87 \\ \bar{Y}=\frac{995}{8}=124.37 \end{gathered}

Replace these values in the formula and find the regression equation as follows:

\begin{gathered} Y-124.37=4.6(X-20.87) \\ Y-124.37=4.6X-4.6\cdot20.87 \\ Y=4.6X-96.11+124.37 \\ Y=4.6X+28.26 \end{gathered}

The answer is a) y=4.6x+28.26

7 0
2 years ago
A rectangular garden has a walkway around it. The area of the garden is 4​(4.5xplus1.5​). The combined area of the garden and th
Arte-miy333 [17]

Answer:

Walkway is 1.5 units²

Step-by-step explanation:

Just subtract the area of the garden from the combined area:

<u>5.5-4=1.5</u>

Also did you mean difference? I don't know what it means by sum.

8 0
3 years ago
Other questions:
  • A school conducts 27 test and 36 weeks assume the school conducts test at a constant rate what is the slope of the line that rep
    9·2 answers
  • Solve for X:
    10·1 answer
  • What is the approximate volume of a right cone with a diameter of 10 meters and a height of 5 meters? Use 3.14 for π.
    5·1 answer
  • A framed picture 24 inches wide and 28 inches high is shown in the diagram below
    6·1 answer
  • Suppose y varies directly with x. Write a direct variation equation that relates x and y. Then find the value of y when x=16...
    11·2 answers
  • Ricardo bought 3 pounds of gummy bears for $7.77. What is price per pound for the gummy bears?
    15·2 answers
  • I need some help please :)​
    15·1 answer
  • Find the slope and the y-intercept of the graph of the linear equation. Then, graph the equation.
    15·1 answer
  • Why does a rectangle with different side lengths have only 2 lines of symmetry?
    14·1 answer
  • For what value of x must ABCD be a parallelogram? 14-7=12x+1
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!