Quantcast

A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

shaqadry

  • 2 years ago

The population of a town grows at a rate proportional to the population present at time t. The initial population of 5000 people is increased by 15% in the period of 10 years. What will the estimated population be in 30 years time?

  • This Question is Open
  1. HawkCrimson
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    have any ideas wat to do? :)

  2. HawkCrimson
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    or how to start off?

  3. Peter14
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    do you know an equation that works for this kind of thing?

  4. HawkCrimson
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    no need for one

  5. Peter14
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    but it's helpful

  6. shaqadry
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes. i work it out until i got P = Ae^(0.15t)

  7. HawkCrimson
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    since 10yrs=15% then 30yrs=45% thus the population growth in 30 yrs is 5000 x 145/100 50 x 145

  8. Peter14
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the equation you can find for this problem is\[P=5000 \times 1.15^\frac{ t }{ 10 }\]

  9. Peter14
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    then you plug in 30 for t

  10. HawkCrimson
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    wat is the denominator under t?

  11. HawkCrimson
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    lol the shortcut is easier and less complicated :P ur just jelly

  12. Peter14
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    nevermind, @HawkCrimson the shortcut you took doesn't work

  13. HawkCrimson
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    D: haha

  14. shaqadry
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @Peter14 i dont understand...can you show me how it starts from P = Ae^(0.15t) ?

  15. Peter14
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    what you actually do each 10 years is you multiply the number of people by 1.15

  16. HawkCrimson
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    cause it's 15%= . 15 right? :D

  17. shaqadry
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    where does 1.15 come from?

  18. HawkCrimson
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh ik how to do it by the shortcut way :P but it's long and tedius

  19. Peter14
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    1.15 is 115% the way the problem expresses this is as an exponential growth problem.

  20. shaqadry
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    but the question says 15% :/

  21. Peter14
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the shortcut you took would work for an arithmetic sequence (meaning you add a certain amount each time) but this is a geometric sequence (meaning you multiply by a certain amount each time.

  22. HawkCrimson
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    lol forget me, answer the girl :P

  23. HawkCrimson
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    100%=5000 pop so if it has a pop increase by 15% then it will become 115% that is y

  24. Peter14
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the question says the population increases by 15% each time. The number you get shouldn't decrease at all. Let's look at the first case. If you multiply 5000 by 15% you get the increase in population: 750 people. You can then add that to 5000 to get 5750. or on the other hand, you can multiply 5000 by 115% (because 115% is 100%+15%) and that gives you 5750 with only one operation.

  25. shaqadry
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    okay..

  26. Peter14
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    have you looked at compound interest in your math class or should I try to explain that to you?

  27. shaqadry
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    how do i calculate using the formula dP/dt = kP ?

  28. Peter14
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    o.o where is that from?

  29. Peter14
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    try this http://qrc.depaul.edu/StudyGuide2009/Notes/Savings%20Accounts/Compound%20Interest.htm

  30. shaqadry
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    its the formula given

  31. Peter14
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    what math class are you in?

  32. shaqadry
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i mean thats what we study in application of first order differential equations

  33. shaqadry
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    from that formula we integrate and so on

  34. Peter14
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    wow, you've confused me.

  35. HawkCrimson
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    XD

  36. Peter14
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    and google is sooo slow here in china so I have to stay confused...

  37. Peter14
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok, I understand now. you were given dP/dt = kP as the equation at the beginning. I get it.

  38. Peter14
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    what was the exact wording of the problem? I seem to have misunderstood it before.

  39. shaqadry
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i just want to know how do i start from P=Ae^(0.15t) from what i integrated from the above formula

  40. Peter14
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    what does A represent?

  41. Peter14
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I think T would be 3, because it seems from the description at the top that T is in intervals of 10 years and then P looks like your final population

  42. shaqadry
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yeaa tried that but couldnt seem to get the answer right :/

  43. shaqadry
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    http://fym.la.asu.edu/~pvaz/mat272/ch_07.pdf

  44. HawkCrimson
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    wats the answer?

  45. shaqadry
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    7604 people

  46. Peter14
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you get that using the formula for compound interest, but I think they want you to show your work from using the methods they give you

  47. HawkCrimson
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i got that using the shortcut method but that wont get u any marks in the exam, ill try using the formulae

  48. Peter14
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    maybe you need to find the annual rate of increase instead of the rate of increase for 10 years

  49. shaqadry
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    okay i'll try

  50. HawkCrimson
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    P = Ae^0.15t P = 5000e^0.15(3) P = 7841 :/

  51. shaqadry
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    do i have to find a new rate or what?

  52. Peter14
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes, you do and I know by doing some graphing tricks that the rate ends up approximately 0.013975, but I don't know exactly how you get that numerically. It should have something to do with ln something.

  53. Peter14
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so in the textbook chapter you posted the final equation is P=A(e^kt) you are trying to find k given t=30 and a=5000 do they give you P? I guess what i'm trying to say is, what exactly do they give you at the start of the problem?

  54. shaqadry
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i got it! thanks guys for the help :)

  55. Peter14
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I think you got it less because of us and more despite us.

  56. shaqadry
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    but you guys made it more clear so thanks :D

  57. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.