A house cost $120,000 when it was purchased. The value of the house increases by 10% each year. Find the rate of growth each month.

Answers

Answer 1

Answer: FIRST MODEL:

Well the model for the value of the house is:

$V={ \left( \frac { 11 }{ 10 } \right) }^( t )\cdot 120000$

V = Value

t = Years passed {t≥0}

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When t=0, V=120000

When t=1, V=132000

When t=2, V=145200

etc... etc...

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Now, this model is actually curved so there is no constant rate of growth each month. We can only calculate what the rate of growth is at a particular time. If we want to find out the rate of growth at a particular time, we must differentiate the formula (model) above.

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$V={ \left( \frac { 11 }{ 10 } \right) }^( t )\cdot 120000\n \n \ln { V=\ln { \left( { \left( \frac { 11 }{ 10 } \right) }^( t )\cdot 120000 \right) } }$

$\n \n \ln { V=\ln { \left( { \left( \frac { 11 }{ 10 } \right) }^( t ) \right) } } +\ln { \left( 120000 \right) } \n \n \ln { V=t\ln { \left( \frac { 11 }{ 10 } \right) } } +\ln { \left( 120000 \right) }$

$\n \n \frac { 1 }{ V } \cdot \frac { dV }{ dt } =\ln { \left( \frac { 11 }{ 10 } \right) } \n \n V\cdot \frac { 1 }{ V } \cdot \frac { dV }{ dt } =\ln { \left( \frac { 11 }{ 10 } \right) } \cdot V$

$\n \n \therefore \quad \frac { dV }{ dt } =\ln { \left( \frac { 11 }{ 10 } \right) } \cdot { \left( \frac { 11 }{ 10 } \right) }^( t )\cdot 120000$

Plug any value of (t) that is greater than 0 into the formula above to find out how quickly the investment is growing. If you want to find out how quickly the investment was growing after 1 month had passed, transform t into 1/12.

The rate of growth is being measured in years, not months. So when t=1/12, the rate of growth turns out to be 11528.42 per annum.

SECOND MODEL (What you are ultimately looking for):

$V={ \left( \frac { 11 }{ 10 } \right) }^{ \frac { t }{ 12 } }\cdot 120000$

V = Value of house

t = months that have gone by {t≥0}

Formula above differentiated:

$V={ \left( \frac { 11 }{ 10 } \right) }^{ \frac { t }{ 12 } }\cdot 120000\n \n \ln { V } =\ln { \left( { \left( \frac { 11 }{ 10 } \right) }^{ \frac { t }{ 12 } }\cdot 120000 \right) }$

$\n \n \ln { V=\ln { \left( { \left( \frac { 11 }{ 10 } \right) }^{ \frac { t }{ 12 } } \right) } } +\ln { \left( 120000 \right) }$

$\n \n \ln { V=\frac { t }{ 12 } } \ln { \left( \frac { 11 }{ 10 } \right) } +\ln { \left( 120000 \right) }$

$\n \n \frac { 1 }{ V } \cdot \frac { dV }{ dt } =\frac { 1 }{ 12 } \ln { \left( \frac { 11 }{ 10 } \right) }$

$\n \n V\cdot \frac { 1 }{ V } \cdot \frac { dV }{ dt } =\frac { 1 }{ 12 } \ln { \left( \frac { 11 }{ 10 } \right) } \cdot V$

$\n \n \therefore \quad \frac { dV }{ dt } =\frac { 1 }{ 12 } \ln { \left( \frac { 11 }{ 10 } \right) } \cdot { \left( \frac { 11 }{ 10 } \right) }^{ \frac { t }{ 12 } }\cdot 120000$

When t=1, dV/dt = 960.70 (2dp)

dV/dt in this case will measure the rate of growth monthly. As more money is accumulated, this rate of growth will rise. The rate of growth is constantly increasing as the graph of V is actually a curve. You can only find out the rate at which the house value is growing monthly at a particular time.

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Answers

Answer:

Yes. The outcomes can be classified into two categories, the trials are fixed, and the events are independent.

Step-by-step explanation:

Hope this helps!!

A number, n, is added to 15 less than 3 times itself. The result is 101. Which of the following can be an equation can be used to find the value of n?a.n + (3n - 15) = 101
b.4n - 15 = 101

Answers

Answer:

Option a and b both are correct.

Step-by-step explanation:

We have been given the information that is: n is added to 15 less than 3 times itself.

The result is 101.

So, the number is 15 less than 3 times to itself means: 3n-15

And n is added to it that means:

n+(3n-15)

And its result is 101 so,

n+(3n-15)=101

After simplification of above expression gives:

4n-15=101.

Therefore, Option a and b both are correct.

Which answer is the most reasonable estimation?Cylvia is making 100 sandwiches for a banquet. She makes 47 sandwiches. Then she takes a break and makes 22 more. About how many more sandwiches does Cyliva have to make?

A.about 80

B.about 40

C.about 70

D.about 30

Answers

the answer is c about 70.she has 69 left

Dee spends $0.25, $0.30, $0.10 and $0.04.

How much $ does she spend in all?

Answers

By adding all the money she spend we get $0.69

What is the unitary method?

The unitarymethod is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We are given that Dee spends $0.25, $0.30, $0.10 and $0.04.

We need to find the money she spend in all.

Therefore, we have to add all the expenditure

0.25 + 0.30 + 0.10 + 0.04 = 0.69

The total money she spend could be 0.69.

Learn more about the unitary method, please visit the link given below;

brainly.com/question/23423168

#SPJ2

answer: $0.69

explanation: 0.25 + 0.30 + 0.10 + 0.04 = 0.69

If (x + 2 ) is a factor of x3 − 6x2 + kx + 10, k =

Answers

If a binomial x-a is a factor of a polynomial p(x), then p(a)=0.

x+2 is a factor of p(x)=x³-6x²+kx+10, so p(-2)=0.

$p(-2)=0 \n(-2)^3 - 6 * (-2)^2 + k * (-2) + 10=0 \n-8-6 * 4-2k+10=0 \n-8-24-2k+10=0 \n-2k-22=0 \n-2k=22 \nk=(22)/(-2) \n\boxed{k=-11}$

Answer:

-11

Step-by-step explanation:

128 is 74% of what number if necessary round your answer to the nearest hundredth

Answers

74% * x = 128
x=128/74%
x=172.97 (nearest hundredth)

Steps:
1. Do a proportion
128/x=74/100
2. Do 128 times 100 which equals 12,800
3. Do 12,800 divided by 74 which equals 172.972
4. If you rounded to the nearest hundreth, your answer would be: 172.97
(Since the 2 after the 7 was below 5, you would round down to 7)

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