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
finlep [7]
2 years ago
7

The population of a certain community is known to increase at a rate proportional to the number of people present at time t. If

the population has doubled in 5 years, how long will it take to triple?
Mathematics
1 answer:
attashe74 [19]2 years ago
4 0

Answer:

t=7.85 years

Step-by-step explanation:

We can write this rate as an ordinary differential equation.

\frac{dP}{dt}=aP

Where a is proportional constant, P the population variable, and t the time.

\frac{dP}{P}=adt

Integrating each side of the equation.

\int \frac{dP}{P}=\int adt

ln(P)=at+c

P=e^{at+c}

P=e^{c}e^{at}=Ce^{at}

To find C we need to use the initial condiction, it means evaluae P at t=0.

P_{0}=Ce^{0}=C

P=P_{0}e^{at}

Now, we use the sentence  the population has doubled in 5 years.

2P_{0}=P_{0}e^{a5}

We can find "a" in this condition.

2=e^{a5}

ln(2)=a5

a=\frac{ln(2)}{5}

a=0.14

Finally, let's find how long will it take to triple.

3P_{0}=P_{0}e^{0.14t}

3=e^{0.14t}

t=\frac{ln(3)}{0.14}

t=7.85 years

I hope it helps you!

You might be interested in
Estimate the square root of the imperfect square of 18.
ludmilkaskok [199]

Answer:

18 times four is 72

Step-by-step explanation:

3 0
3 years ago
a wheel has a diameter of 15cm. The wheel travels 50 metres. How many revolutions does the wheel complete?
TEA [102]

Answer:

106

Step-by-step explanation:

The diameter of the wheel is 15 cm or 0.15 m.

The circumference of the wheel is 0.15π m ≈ 0.47 m.

So the wheel moves 0.47 m with each revolution.

The wheel travels 50 m, so the number of revolutions is:

(50 m) / (0.47 m/rev) ≈ 106 revolutions.

8 0
2 years ago
To round the number to the hundredths place, what should be done first?
Oksanka [162]

Answer:

b

Step-by-step explanation:

5 0
3 years ago
Help me on this question
tatyana61 [14]

Answer:

The single transformation that maps shape A into shape B is 4 steps right and 3 steps down.

8 0
3 years ago
Solve for r: i=prt<br> please help
babymother [125]

Answer:

hmm

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Other questions:
  • Find the value of x
    12·1 answer
  • This water tank is made from a cylinder cone what is the volume of the tank<br><br> HELP PLEASE
    5·1 answer
  • 4. Simplifyi the following fraction 4/8
    5·2 answers
  • What is its equation???
    9·2 answers
  • PLZ HELP ME THANKS. If 3x-5-6x-2 is equaled to -1. Then how do I "check it"?
    5·2 answers
  • When the base of the ladder is 10 ft away from the base of a building, the top of the ladder touches the building 18 ft above th
    8·1 answer
  • 3(m+15)=5(m-10)+35 HELP
    13·1 answer
  • Does y = -5x represent a proportional relationship?
    8·1 answer
  • find the coordinates of the point where the graph of the following function intersects the x axis y=x^2-5x+6/x-2
    8·1 answer
  • 4 less than four times a number is equal to three times the same number plus 1
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!