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Dafna1 [17]
3 years ago
10

The population of a county is growing at a rate of 9% per year, compounded continuously. How many years will it take for the pop

ulation to quadruple according to the exponential growth function? Round your answer up to the nearest whole number, and do not include units.
Mathematics
1 answer:
Liula [17]3 years ago
6 0

It will take 15 years for the population to quadruple

Step-by-step explanation:

The formula for continuously compounding rate is  A=Pe^{rt} , where

  • A is the future amount
  • P is the initial amount
  • r is the interest as a decimal
  • t is the time in years

Assume that the initial population is P

∵ The initial population = P

∵ The growth rate = 9% ⇒ compounded continuously

∴ r = \frac{9}{100} = 0.09

∵ The population will quadruple in t years

∴ A = 4P

- Substitute these values in the formula

∵ A=Pe^{rt}

∴ 4P=Pe^{(0.09)t}

- Divide both sides by P

∴ 4=e^{0.09t}

- Insert ㏑ to both sides

∴ ㏑(4) = ㏑( e^{0.09t} )

∵ ㏑( e^{n} ) = n

∴ ㏑ (4) = 0.09 t

- Divide both sides by 0.09

∴ t = 15.4

∴ t = 15 years to the nearest whole number

It will take 15 years for the population to quadruple

Learn more:

You can learn more about the logarithmic function in brainly.com/question/11921476

#LearnwithBrainly

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Suppose that the data for analysis includes the attributeage. Theagevalues for the datatuples are (in increasing order) 13, 15,
Bas_tet [7]

Answer:

a) \bar X = \frac{\sum_{i=1}^{27} X_i }{27}= \frac{809}{27}=29.96

Median = 25

b) Mode = 25, 35

Since 25 and 35 are repeated 4 times, so then the distribution would be bimodal.

c) Midrange = \frac{70+13}{3}=41.5

d) Q_1 = \frac{20+21}{2} =20.5

Q_3 =\frac{35+35}{2}=35

e) Min = 13 , Q1 = 20.5, Median=25, Q3= 35, Max = 70

f) Figura attached.

g) When we use a quantile plot is because we want to show the percentage or the fraction of values below or equal to an specified value for the distribution of the data.

By the other hand the quantile-quantile plot shows the quantiles of the distribution values against other selected distribution (specified, for example the normal distribution). If the points are on a straight line we assume that the data values fit very well to the hypothetical distribution selected.

Step-by-step explanation:

For this case w ehave the following dataset given:

13, 15, 16, 16, 19, 20, 20, 21, 22, 22, 25, 25, 25, 25, 30,33, 33, 35, 35, 35, 35, 36, 40, 45, 46, 52, 70.

Part a

The mean is calculated with the following formula:

\bar X = \frac{\sum_{i=1}^{27} X_i }{27}= \frac{809}{27}=29.96

The median on this case since we have 27 observations and that represent an even number would be the 14 position in the dataset ordered and we got:

Median = 25

Part b

The mode is the most repeated value on the dataset on this case would be:

Mode = 25, 35

Since 25 and 35 are repeated 4 times, so then the distribution would be bimodal.

Part c

The midrange is defined as:

Midrange = \frac{Max+Min}{2}

And if we replace we got:

Midrange = \frac{70+13}{3}=41.5

Part d

For the first quartile we need to work with the first 14 observations

13, 15, 16, 16, 19, 20, 20, 21, 22, 22, 25, 25, 25, 25

And the Q1 would be the average between the position 7 and 8 from these values, and we got:

Q_1 = \frac{20+21}{2} =20.5

And for the third quartile Q3 we need to use the last 14 observations:

25, 30,33, 33, 35, 35, 35, 35, 36, 40, 45, 46, 52, 70

And the Q3 would be the average between the position 7 and 8 from these values, and we got:

Q_3 =\frac{35+35}{2}=35

Part e

The five number summary for this case are:

Min = 13 , Q1 = 20.5, Median=25, Q3= 35, Max = 70

Part f

For this case we can use the following R code:

> x<-c(13, 15, 16, 16, 19, 20, 20, 21, 22, 22, 25, 25, 25, 25, 30,33, 33, 35, 35, 35, 35, 36, 40, 45, 46, 52, 70)

> boxplot(x,main="boxplot for the Data")

And the result is on the figure attached. We see that the dsitribution seems to be assymetric. Right skewed with the Median<Mean

Part g

When we use a quantile plot is because we want to show the percentage or the fraction of values below or equal to an specified value for the distribution of the data.

By the other hand the quantile-quantile plot shows the quantiles of the distribution values against other selected distribution (specified, for example the normal distribution). If the points are on a straight line we assume that the data values fit very well to the hypothetical distribution selected.

6 0
3 years ago
Please help this is so difficult
White raven [17]

Answer:

B

Step-by-step explanation:

For a line to be parallel it must have the same slope

6x-2y=-5

+5        +5

6x-2y+5 = 0

   +2y       +2y

6x+5  =2y

/2        /2

3x+5/2=y                  So the slope is 3 and we know it can only be either B or D

Now we need to find which line passes through (7,-2) and we find this by plugging 7 into B and D

B. -2= 21-23 TRUE

D. -2 = 21+ 23 FALSE

So the answer is B

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3 years ago
Identify the slope for each tables below .....Help me
LenaWriter [7]
The slope of number 9 equals 0, becuase it is horizontal.
The slope of number 10 equals.
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6 0
3 years ago
The sales tax in your state is 5% if a car costs $24,600 what is the total cost including tax?
Svetach [21]
<h2>Greetings!</h2>

Answer:

$25830

Step-by-step explanation:

If 100% of the car price is 24,600 , then you can imagine that extra 5% being added to this

100 + 5 = 105

So you need to find what 105% of the cost was.

To do this you can use the percentage formula:

Amount x \frac{percentage}{100}

Now, you can simply plug the values into this

24,600 x \frac{105}{100}

24600 x 1.05 = 25830

<h3>So the total cost including tax would be $25830!</h3><h3 /><h2>Hope this helps!</h2>
7 0
3 years ago
If tile costs $8.50 per square foot, how much does it cost per inch?
Sphinxa [80]

Answer:

$0.06 per square inch

Step-by-step explanation:

The question should be:

<em>"If tile costs $8.50 per square foot, how much does it cost per square inch?"</em>

<em />

To solve this, we basically need a conversion from feet to inches. BUT 2 times, since we are talking about "square feet" and "square inches".

We know 1 feet = 12 inches

Also, since we are going from square feet to square inches [big to small], we have to divide TWICE.

Thus, we will have:

\frac{8.5}{12*12}

We are dividing 8.5 (the cost) by 12, 2 times since we want square feet in square inches. The answer is:

\frac{8.5}{12*12}=0.06

So, tile costs $0.06 per square inch

6 0
3 years ago
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