Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

andreadesirepen

  • 2 years ago

How do I write a half life function of this info? F(x)=45e^-.89x y=45e^-.89x y/45 = e^(-.89x) in y/45 = In e^(-.89x) in y - in 45 = in e^-.89x in y = in e^-.89x+3.81 in y = -.89x+3.81

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

    HELP! It says it should look like this: F(x)=A(1/2)^x. Where A is the initial amount of the substance and x represents the time for decay. I have A, it´s 25. How do i find x?

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

    if:\[F(x)=45e^{-.89x}\]then the value of F(0) will tell you how much the initial amount is equal to. In this case it would be:\[F(0)=45*e^0=45\]

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

    what you need to find is the value of x to get half this value

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

    i.e. what value of x will give you F(x) = 22.5

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

    So it would be, 45(1/2)^22.5 ?

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

    no, you need to solve the equation:\[22.5=45*e^{-0.89x}\]

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

    this will give you a value for x for which F(x) is equal to half its initial value

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

    i plugged, 45*e^-.89 into my calculator and got 18.5. is that right?

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

    how does that solve the equation I listed above?

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

    you need to rearrange that equation to get an expression for x

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

    I can show you the first few steps...

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

    so, starting with:\[22.5=45*e^{-0.89x}\]we divide both sides by 45 to get:\[0.5=e^{-0.89x}\]then take logs of both sides to get:\[\ln(0.5)=-0.89x\]can you do the rest?

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

    I´m lost sorry, no.

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

    which part are you stuck on?

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

    what to do next

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

    do you understand that you need to find x?

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

    did you follow the reasoning above?

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

    i understand i need to find x, but i dont understand how

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

    If I said:\[12=4x\]then would you be able to find the value of x here?

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

    yes

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

    3

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

    good, so now use the same principals to solve this for x:\[\ln(0.5)=-0.89x\]

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

    i got -.56

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

    tat does not look right to me - please show me your steps so that I can check where you may have made a mistake

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

    *that

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

    i divided .5 by -.89 or is it the other way around?

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

    you cannot do that - the left-hand-side of the equals sign has \(\ln(0.5)\) not just 0.5

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

    so first find the value for \(\ln(0.5)\), then divide that by -0.89

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

    .78

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

    that looks more like it.

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

    is that x?

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

    yes - you can double check that you have the right value for x by substituting it into your original equation:\[F(x)=45e^{-.89x}\]and see if you get roughly 22.5 as the answer.

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

    why would my A be 45?

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

    45(1/2)^.78

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

    In the function given to you, the value of the function when x=0 is 45.

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

    is that the half life function?

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

    no

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

    oh mah gaaahh. this is tuff

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

    In general you ay have an exponentially decaying function defined as:\[F(x)=Ae^{-bt}\]

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

    in this function t represents the time

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

    and you can see (I hope) that when t=0 F(0)=A

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

    so A represents the initial amount - i.e. the amount at the start

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

    as time passes, the mount decays and gets less and less

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

    *amount

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

    at some point, it decays to half its original value

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

    so, at that point F(t) = A/2

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

    now, since we know that:\[F(t)=Ae^{-bt}\]then we can replace F(t) by A/2 to get:\[\frac{A}{2}=Ae^{-bt}\]divide both sides by A to get:\[\frac{1}{2}=e^{-bt}\]take logs of both sides to get:\[\ln(0.5)=-bt\]divide both sides by -b to get:\[t=-\frac{\ln(0.5)}{b}\]this is what the half life is

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

    it represents the amount of time that has to elapse before the amount of material decays to half its original value

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

    I understand the process but it tells me that it needs to look like this: A(1/2)^x

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

    I don't know where you are getting that from - it makes no sense to me.

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

    The half-life of a substance is the time it takes for half of the substance to decay. The exponential function representing half-life is f(x) = A(1/2) where A is the initial amount of the substance and x represents the time for decay. The half-life of the substance will depend on the initial amount of substance you have. In this activity, you will experience this formula in action.

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

    I had to use pennies in the beggining if that helps, so i thought that was A, i used 25 pennies.

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

    where you wrote: f(x) = A(1/2) that corresponds to what I said above when I said that at its half life: so, at that point F(t) = A/2

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

    what this is saying is that when the material (whatever it may be) reaches its half life, then the value of the function f(x) will be equal to HALF the value of f(0). and we know that f(0) = A so, at its half life, f(x) = A/2

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

    that´s the function? why doesnt it look like f(x) = A(1/2)^x ?

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

    it is saying that the VALUE of the function will equal A/2

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

    e.g. if I had a function defined as:\[f(x)=x^2\]and I asked you to find the value of x for which f(x) = 16, then you would do:\[16=x^2\]therefore:\[x=\sqrt{16}=4\]

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

    so note here that I said you need to find the value of x for which: f(x) = 16

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

    so here we are saying that the VALUE of f(x) should be equal to 16

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

    regardless of how the function itself is defined

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

    So how will the half life equation of my probelm look? like this f(x) = A/2 ?

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

    the HALF LIFE is defined as the point at which the VALUE of the function is equal to half its initial value - i.e. the point at which f(x) = A/2

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

    this is not stating that the FUNCTION definition is f(x) = A/2 instead it is stating that the VALUE of f(x) = A/2 and you need to find a suitable x for this to be true

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

    I need to go now - it is very late here and I need some sleep - hope you understand this concept better now.

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

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

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.