The population of a community is known to increase at a rate proportional to the number of people present at time t. If an initial population P0 has doubled in 3 years, how long will it take to triple? (Round your answer to one decimal place.)

Answers

Answer 1

Answer:

4.75 years are required to triple the population

Step-by-step explanation:

As we know

[tex]\frac{dP}{dt} = P\\[/tex]

Integrating both the side with respect to t we get

[tex]ln P = kt + c_1\\P = e^{kt + c_1}\\P = Ce^{kt}[/tex]

At t = 0, P = P0

[tex]2 P_0 = P_0 * e ^{3k}\\2 = e ^{3k}\\ln 2 = 3k\\k = 0.231\\[/tex]

substituting K value in main equation, we get -

[tex]P = P_0 * e^{0.231 * t}\\3P_0 = P_0 * e^{0.231 * t}\\3 = e^{0.231 * t}\\ln 3 = 0.231 * t\\t = 4.75[/tex]

4.75 years are required to triple the population


Related Questions

The manager of an apartment complex ordered the air conditioners in the apartments to be replaced. The list shows how many years each air conditioner had been in service
11.8, 11.9, 11.9, 12.2, 12.3, 12.9, 13.3, 13.4, 13.6 13.7

What is the median number of years that an air conditioner had been in service?

Answers

Answer:

12.6 years

Step-by-step explanation:

Once you have these written out you kinda just have to look for the middle one and in this that is 12.3 and 12.9 so you add them and then divide by 2. When you add them you get 25.2 and when you divide by 2 you get 12.6. So the median of this data set is 12.6.

Calculate the sample mean and sample variance for the following frequency distribution of heart rates for a sample of American adults. If necessary, round to one more decimal place than the largest number of decimal places given in the data. Heart Rates in Beats per Minute Class Frequency 51 - 58 6 59 - 66 3 67 - 74 11 75 - 82 13 83 - 90 4

Answers

Answer:

[tex]Mean = 68.9[/tex]

[tex]s^2 =18.1[/tex] --- Variance

Step-by-step explanation:

Given

[tex]\begin{array}{cccccc}{Class} & {51-58} & {59-66} & {67-74} & {75-82} & {83-90} \ \\ {Frequency} & {6} & {3} & {11} & {13} & {4} \ \end{array}[/tex]

Solving (a): Calculate the mean.

The given data is a grouped data. So, first we calculate the class midpoint (x)

For 51 - 58.

[tex]x = \frac{1}{2}(51+58) = \frac{1}{2}(109) = 54.5[/tex]

For 59 - 66

[tex]x = \frac{1}{2}(59+66) = \frac{1}{2}(125) = 62.5[/tex]

For 67 - 74

[tex]x = \frac{1}{2}(67+74) = \frac{1}{2}(141) = 70.5[/tex]

For 75 - 82

[tex]x = \frac{1}{2}(75+82) = \frac{1}{2}(157) = 78.5[/tex]

For 83 - 90

[tex]x = \frac{1}{2}(83+90) = \frac{1}{2}(173) = 86.5[/tex]

So, the table becomes:

[tex]\begin{array}{cccccc}{x} & {54.5} & {62.5} & {70.5} & {78.5} & {86.5} \ \\ {Frequency} & {6} & {3} & {11} & {13} & {4} \ \end{array}[/tex]

The mean is then calculated as:

[tex]Mean = \frac{\sum fx}{\sum f}[/tex]

[tex]Mean = \frac{54.5*4+62.5*3+70.5*11+78.5*13+86.5*4}{6+3+11+13+4}[/tex]

[tex]Mean = \frac{2547.5}{37}[/tex]

[tex]Mean = 68.9[/tex] -- approximated

Solving (b): The sample variance:

This is calculated as:

[tex]s^2 =\frac{\sum (x - \overline x)^2}{\sum f - 1}[/tex]

So, we have:

[tex]s^2 =\frac{(54.5-68.9)^2+(62.5-68.9)^2+(70.5-68.9)^2+(78.5-68.9)^2+(86.5-68.9)^2}{37 - 1}[/tex]

[tex]s^2 =\frac{652.8}{36}[/tex]

[tex]s^2 =18.1[/tex] -- approximated

Answer the question plz

Answers

Answer:

F=122 g=58 h=122

Step-by-step explanation:

F and h have same angle

H is same angle as 58

How to when me when i when i

Answers

Shrek plz shrek yes shrek plz shrek yes

Answer:

shrek

Step-by-step explanation:

1+1=2

In a triangle shown, which shows the correct order of the side lengths from smallest to largest.
A= 65 degrees B= 80 degrees C= 35 degrees

Answers

Answer:

Not sure if there are options, but the order of side lengths from smallest to largest is j, k, l

Step-by-step explanation:

This is a bad explanation (sorry):

Side length order will be the same order of angle orders. By that, I mean the since angle C has the smallest angle, the side length across from it will also be the smallest. Since angle B is the biggest angle, side L will be the biggest length. This leaves angle A (and side k) in the middle.


Sully saves 2/3 of her paycheck for bills. If she makes $1,983, how much does she
have to pay her bills?

Answers

Answer:According to the rule, you should be spending no more than 43 percent of your before-tax income on all your debt payments. So, if your gross income per month is $4,000, your total debt including mortgage, auto loans, credit card payments and student loans should be less than $1,720

Step-by-step explanation:

A model of the Pythagorean Theorem is shown.



169 square units. 144 square units. 25 square units.



Based on the information in the model, which equation represents the Pythagorean theorem?

Answers

Answer:

Step-by-step explanation:

help me pls pls pls

Answers

D (pause)

the answer is D

the last oneee

If a customer left a $5 tip for a bill that had a subtotal of $31.25 what percent tip did the customer leave?

Answers

Answer:

16%

Step-by-step explanation:

= (5/31.25)*100=16%

Plz help me ive been stuck on this for 30 minutes

George sold 18, 22, 26, 12, 25, 20, and 19 cars per month over the past seven months. He followed the steps below to determine the number of cars he needs to sell in the next month to have a mean number of sales per month of 24.

Step 1: Find the total cars needed to have a mean of 24: 24 times 7 = 168.
Step 2: Find the total cars sold: 18 + 22 + 26 + 12 + 25 + 20 + 19 = 142.
Step 3: Subtract the total cars sold from the total cars needed: 168 minus 142 = 26.
Step 4: State the answer: George needs to sell 26 cars next month.

Where did George make his first mistake?
Step 1
Step 2
Step 3
Step 4

Answers

Answer:

Step One. He should have multiplied by 8.

HELPPP I NEED TO DO THIS BEFORE 7:00​

Answers

Answer:

A, (13/3 x 5/13)

Step-by-step explanation:

So first, you should change the mixed numbers into improper fractions.  To convert, just multiply the whole number by the denominator and add the numerator.  Do that to both fractions and you should get 13/3 ÷ 13/5.  Since you need to switch to multiplication, switch the sign and flip that fraction/  That asnwer is 13/3 x 5/13.  Hope that helps!  :)

We’re they right above

What is the missing number?
29=(30-6)+?

Answers

Answer:

5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

30-6=24

29-24= 5

What is the difference of 78−13?

Answers

Answer:

65

Step-by-step explanation:

According to the 2006 Uniform Crime Report (UCR), the state of Delaware had a population of 853,476 and 5,817 violent crimes. Compute the violent crime rate per 100,000 persons and interpret your result.

Answers

Answer:

682

Step-by-step explanation:

Population = 853,476

Number of violent crimes = 5817

We are to get violent crime rate per 100000 persons and interpret the result obtained.

Now if population is 1

Crime = 5817/853476

If population is 100000,

Crime = 5817x100000/853476

= 681.56

= 682

We conclude that the violent crime rate is of 682 crimes per 100000

Jared and his six friends put their names in a bag to randomly select a driver for their weekly carpool. What is the probability that Jared will be selected to be the driver for the upcoming week?

Answers

The probability of Jared being picked would be 1/7, being that he and his 6 friends are drawing out of the bag.

Judy plans to serve cheese to guests at a dinner party. She estimates
each guest will have 2 ounces of cheese, and she wants to have 8
additional ounces of cheese available. If Judy has 40 ounces of cheese,
which expression can be used to determine the number of guests Judy
can invite to her party?

Answers

Answer:

4

Step-by-step explanation:

2+8 = 10

10/40 = 4

4

Maybe...

Bagel Boys delivers bagels for a $6
delivery fee plus $2.50 per bagel. An
engineering firm has $100. What is the
maximum number of bagels the firm
can purchase?
A. 37 bagels B. 38 bagels
C. 39 bagels D. 40 bagels

Answers

Answer:

A.37 BAGELS

Step-by-step explanation:

100-6

94/2.50

37.6 round down

37 bagels

Help me plsss in need help there is a picture

Answers

Answer:

Division Expression - 7 ÷ 3

Unit Form - 21 thirds ÷ 3 = 7

Improper Fraction 7/3

Step-by-step explanation:

Hope this helps!! <3

Pls help I’m failing asap

Answers

Answer:

The equation 2d + 18 = 24 can help find the number of days Jerry has been doing sit-ups.

Step-by-step explanation:

During the first day, Jerry did 18 sit-ups, and he proceeded to do 2 more sit-ups each following day, so the expression to represent this situation is 2d + 18. Because he did 24 sit-ups today, to find the number of days he did sit-ups, the equation to solve is 2d + 18 = 24.

7. Use the Unit Circle to find the exact value of the trig function,
sin(180°)

Answers

The exact value is 0

There are 6 fourth-grade students, 8 fifth-grade students, and 10 sixth-grade students on the girls’ soccer team at Truman Elementary School. What is the ratio of all students to fourth-grade students? Use a proportion to solve.

Answers

Answer:

Your answer is

Fourth grade student = 25%

Fifth grade= 33.33%

Sixth grade= 41.67%

Want more answer then follow me, like and MARK MY ANSWER AS BRAINLIST ANSWER.

I need that urgently.

so alot of the text got cut off so im going to re wright the problem

An illusionist needs both female and male volunteers for a show he needs no more then 10 volunteers for a show the illusionist needs fewwr then 4 female volunteers let X represent the number of female volunteers and Y represent the number of male volunteers which inqualities model the situation select eatch correct answer​

Answers

Answer:

A. x+y<10

B. x+y≤10

Step-by-step explanation:

A is correct because they can be less than.

B is correct because there is less than or equal too of numbers of volunteers.

C, D, and E cannot be correct however, because that means that they can be over at any number. Therefore, these three would be incorrect.

10.
The circumference of a circular garden is 25 feet. Which of the following expressions best
represents the diameter of the garden?

Answers

Answer:

A) d = 25/π

Step-by-step explanation:

To find the diameter of a circle, refer to the circumference formula:

C = d (π)

25 = d (π)

25/π = d

d = 25/π

- {(-3, 3), (1, 1), (0, -2), (1,-4), (5, -1)}

Function?

Answers

Answer:

Step-by-step explanation:

It is not a function. (1,1) and (1,-4) are both points on the graph.

please answer !!Urgent ​

Answers

I'm sorry I don't know what this is can you explain it sike

Press F9 on your keyboard five more times and see how long Carol lives in each of her alternate lives. Remember that she will always live to be at
least 44 years old, since she is already 44 years old. How long did Carol live each time?

Answers

Answer:

59 or infant

Step-by-step explanation:

she will either live to be 59 each time or she will live to be a undying God like being

59 years Total she will live

3 1/3 x 14 = 3 14/2 =
H3

Answers

Answer:

10?

Step-by-step explanation:

I'm assuming it wants you to simplify 3 14/2 if so, then the answer would be 3 14/2 = 10

[tex]3\frac{1}{3}\cdot \:14 =\frac{10}{3}\cdot \:14 =\frac{10\cdot \:14}{3} =\frac{140}{3} =46\frac{2}{3}[/tex]

Hope I helped you!Success!

1 3 Sophia took home of the pizza that was left over from a party. The amount she took represents of a 8 whole pizza. 3 1 The equation p = can be used to find the number of pizzas p left over from the party. 8 2 How many pizzas were left over? There were pizzas were left over from the party.

Answers

Answer:

Sophia took home 2/5 of the pizza that was left over from a party. The amount she took represents 1/2 of a whole pizza. The equation 2/5p=1/2 can be used to find the number of pizzas p left over from the party.

Step-by-step explanation:

Will got an insurance check of $4500. He deposited it into a savings account at 1.7 percent interest for five years. What was the total amount of money in the account after five years? $4882.50 $4462.50 $4374.38 $4315.63

Answers

Answer:

the answer is 4882.50, hope this helps

Answer the first one plz

Answers

Answer:

65 is the answer okkkkkk

Best of luck

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