A young couple purchases their first new home in 2011 for​ $95,000. They sell it to move into a bigger home in 2018 for​ $105,000. First, we will develop an exponential model for the value of the home. The model will have the form

Answers

Answer 1

Given:

The value of home in 2011 is $95,000.

The value of home in 2018 is $105,000.

To find:

The exponential model for the value of the home.

Solution:

The general exponential model is

[tex]y=ab^x[/tex]       ...(i)

where, a is initial value and b is growth factor.

Let 2011 is initial year and x be the number of years after 2011.

So, initial value of home is 95,000, i.e., a=95,000.

Put a=95000 in (i).

[tex]y=95000b^x[/tex]       ...(ii)

The value of home in 2018 is $105,000. It means the value of y is 105000 at x=7.

[tex]105000=95000b^7[/tex]

[tex]\dfrac{105000}{95000}=b^7[/tex]

[tex]\dfrac{21}{19}=b^7[/tex]

Taking 7th root on both sides, we get

[tex]\left(\dfrac{21}{19}\right)^{\frac{1}{7}}=b[/tex]

Put [tex]b=\left(\dfrac{21}{19}\right)^{\frac{1}{7}}[/tex] in (ii).

[tex]y=95000\left(\left(\dfrac{21}{19}\right)^{\frac{1}{7}}\right)^x[/tex]

[tex]y=95000\left(\dfrac{21}{19}\right)^{\frac{x}{7}}[/tex]

Therefore, the required exponential model for the value of home is [tex]y=95000\left(\dfrac{21}{19}\right)^{\frac{x}{7}}[/tex], where x is the number of years after 2011.


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Answer:

(-5, 4)

Step-by-step explanation:

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It’s (0, 4.5).

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Answer:

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Step-by-step explanation:

Answer:

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i know it

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Answer:

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Step-by-step explanation:

15% of 30000 is (multiply 30000 by .15 to get this) 4500

Subtract 4500 from 30000 and you got the answer

im doing an escape do you think you can help me with the riddle? Who Am I?

I am a member of the Patuxet tribe. I taught the English settlers how to survive the harsh American wilderness. It helped that I spoke the English language. So, I could act as an interpreter between the pilgrims and the native americans. My people taught them how to find medicinal plants, build wigwams, and use fish for fertilizer. Most people know me by ______, but I am also known as Tisquantum.

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Answer:

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What is the length of side A in centimeters?

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Answer:

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Answer:

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Step-by-step explanation: hope it helps!

divide 25/1658 To find the quotient, start by dividing _
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Answer:

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Step-by-step explanation:


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Answers

Answer:

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Step-by-step explanation:

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x1 would be 9, x2 would be -3, y1 would be 2, y2 would be -2. When plugged in, you should get 6/2, and 0/2 for y. When simplified, x would be 3 and y would be 0. This means that the midpoint of the line segment is (3,0)

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Answers

Answer:

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Step-by-step explanation:

Given that :

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A recipe for Potato Soup is listed below:
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that’s a pretty good recipe

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Answer: D. 5%

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Answer:

inear equations Dear Dr Math: I hope you ... 10-(k+5) = 3(k+2) I would also appreciate any explanation. ... So we have to try to get all the "k's" on one side of the equation, and all the ... Let's look at the right side: 3(k+2) Okay, we could say this as 3 times the sum of k and 2.

Step-by-step explanation:

Answer:

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Step-by-step explanation:

I just combined like terms

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Answer:

There were 20 questions on the test.

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Answer:

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Step-by-step explanation:

Answer:

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Answers

Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Answers

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Answers

Answer:

The height of the window = x + 2 = 4.23 + 2= 6.23m

Step-by-step explanation:

The angle of elevation of the top of the house and the window is 60 and 45 degree.

We can proceed as drawing a diagram as a man of height 2m and a building of total height 12m.

draw a horizontal line along the height of a man so that it touches building at height 2mtill the window height we assume its height as 'x' from the man's height.distance till the top from the window will be 'y'

we don't know the distance between man and the building let it be 'b'

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x=b .............(1)

total height of the building is given as 12m

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x + y = 10 .....................(2)

[tex]\frac{x+y}{b} =\frac{x+y}{x }[/tex]  = tan 60

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Answers

Answer:

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Step-by-step explanation:

5x + 5 - 2x - 1

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Answers

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Step-by-step explanation:

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Step-by-step explanation:

Answer:

y = 0x - 4

Step-by-step explanation:

The slope is 0

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Answers

Find the slope of each of the two lines using the formula

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Let me know if this helped!

9514 1404 393

Answer:

  21.  perpendicular

  22.  neither

  23.  parallel

Step-by-step explanation:

It can help to plot the points on a graph and draw lines through them. This can also let you count grid squares, which can make it easier to find the slope.

21. See attachment 1. The lines are perpendicular.

QR has a slope of -3/2. ST has a slope of 2/3, the opposite reciprocal.

__

22. See attachment 2. The lines are neither parallel nor perpendicular.

__

23. The x-coordinates of Q and R are the same, so this is a vertical line at x=-1. The x-coordinates of S and T are also the same, so it is a vertical line at x=11. The two vertical lines are parallel to each other.

_____

Additional comment

When you have a number of problems that all require similar arithmetic, it can be useful to embed that arithmetic in a spreadsheet. You have to enter the numbers somewhere to "show work" or perform a calculation, so you may as well enter them into a spreadsheet that does the calculation for you.

Of course, the slope formula is ...

  m = (y2 -y1)/(x2 -x1)

If you simply show the values of m for each pair of points, you can see if they are equal (lines are parallel). You can also have the spreadsheet compute their product to see if it is -1 (lines are perpendicular). If you get a #DIV/0! error, it means the line is vertical (and the product will also give an error). You can avoid error messages by making the spreadsheet more sophisticated, but that isn't necessary for the purpose here.

I NEED HELP NOW!!! I ONLY HAVE 5 MIN TO TURN THIS IN

Answers

Answer:

a)

28000 + 3000·x = 36000 + 2000·x --> x = 8 years

b)

28000 + 3000·8 = $52000

Answer:

a.  x = 8 yearsb.  52,000

Step-by-step explanation:

company A = 28,000 + 3,000 (x)

company B = 36,000 + 2,000 (x)

where x = no. of years.

company A = company B

28,000 + 3,000 (x) = 36,000 + 2000 (x)

3,000 (x) - 2,000 (x) = 36,000 - 28,000

1,000 (x) = 8,000

x = 8,000

     1,000

x = 8 years

plugin value of x = 8 into company A and B

company A = 28,000 + 3,000 (8)

company A = 52,000

company B = 36,000 + 2,000 (8)

company B = 52,000

PLEASE ANSWER THIS ASAP !!!!

Answers

Answer:

C

Step-by-step explanation:

Answer:

answer is B

Step-by-step explanation:

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