A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

The value, V , of a Tiffany lamp, worth $225 in 1965, increases at 15% per year. Its value in dollars t years after 1965 is given by V=225(1.15)^t Find the average value of the lamp over the period 1965-1993 (INTEGRAL PROBLEM)

  • This Question is Closed
  1. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    225 is a constant, you can pull that aside and focus on 1.15^t

  2. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ln1.15(x) = t try to substitute that

  3. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    not ln...but log1.15(x) = t

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

    why did you take though

  5. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ?

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

    log ...im sorry

  7. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    just thought itd be easier to play with.... I got no objection to another way :)

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

    oh ok...is there a general pattern that i should follow...or even an order

  9. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i think I recall the base other than e stuff now...

  10. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    a pattern..... nothing concrete that I am aware of, just find a function that you can work with easily

  11. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    1.15^t is the derivative of some F(x) what do we know about exponent derivatives?

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

    OMG im so confused

  13. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Dx(5^x) = Dx 5^x right? or am i forgetting something there...which I am prone to do

  14. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    you want to integrate this function right?

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

    yea

  16. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    then we need to "play" around with it to get it into some form that we can work with or recognize that is easy for us right?

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

    oh ok

  18. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    we dont want to change any value to it, just the way it "looks"

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

    alright... so its log 1.15(x)= t {where did u get x from}

  20. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    from the garbage can inthe back of my memory :) i think we should try it another way... I had forgotten about the derivatives or exponential functions other then base "e"

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

    lol..ok

  22. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    lets try to "derive" a function down to something that looks close to our problem, that might help us "remember" thru the cobwebs :)

  23. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    y = 5^x how would we "derive" this? do you recall?

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

    lnx (5^x)

  25. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    you sure? cause it looks right to me...

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

    haha.. i think ...wait let me check

  27. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    remember the steps to get it?

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

    what steps?

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

    it actually is ln(5) 5^x

  30. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    thats better :)

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

    so damn close

  32. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok..now were ready lol

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

    thanks for not bailing on me half way

  34. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so the derivative of 5^t would be?

  35. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i got nowhere to go ....

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

    ln(5)5^t

  37. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    and that is our "key" to this problem

  38. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    if we can get it to "look" like ln(1.15) 1.15^t we can easily integrate it back up right? so how do we change the way something looks without cahnge the value of it?

  39. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    14 times what = 14?

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

    *1

  41. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i knew that number would be useful :) we need a convenient form of the number "1". that has ln(1.15) in it...what would that be?

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

    omg...idk

  43. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    lol ..... what do you know that equals 1?

  44. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    does 4/2 = 1? does 4/3 =1? does 4/4 =1??

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

    ohhh ....4/4?

  46. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    instead of a "4" we need what..... ln(1.15) right?

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

    yea

  48. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    good, lets set up out integrand then...

  49. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    this is our starting point \[\int\limits_{} 225(1.15^t)\]

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

    dont we have to use F(b)-F(a)

  51. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    lets pull out the constants to get this:\[225 \int\limits_{} 1.15^t\]

  52. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    we need to find F(x) before we can use it lol

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

    dang it

  54. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    now lets multiply our integrand by our convenient form of "1"

  55. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[225 \int\limits_{} [\ln(1.15)/\ln(1.15)] 1.15^t\]

  56. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    tell me... is ln(1.15) a constant??

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

    yes

  58. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    then lets pull the bottom one out and leave the top in to use..sound good?

  59. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[225/\ln(1.15) \int\limits_{} \ln(1.15) 1.15^t\]

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

    okay that kinda makes sense

  61. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    now what do we know our integrand will become?

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

    oh shoot ......1.15^t

  63. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    thats correct :) \[F(t) = [225/\ln(1.15)] 1.15^t \]

  64. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    now use your "t" values and figure out the answer :)

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

    ok...i had one more question....so my values are gonna 1 and 28?

  66. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    225 ------- * 1.15^t = F(t) ln(1.15)

  67. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    id subtract 1965 from both years to get a span of time

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

    yeah i subtracted 1965 from 1983

  69. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    1983?? or 1993?

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

    1993...my bad

  71. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    it aint 1 to 28, its.... zero to 28. 1965-1965=0

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

    thats where i was confused .

  73. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    1.15^0 = 1 so that aint a biggy

  74. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah....it was the subtraction that confused ya :) lol

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

    OMG...i got it right...THANK YOU

  76. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    80599.643 - 1609.88 =?

  77. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yay!!! that means im smart ;)

  78. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    we..were smart

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

    yea...u my friend are the man...

  80. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    just dont ask me the hard questions :)

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

    lol...its all good

  82. 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.