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help_people

  • one year ago

Samuel bought a cement mixer for $54,205. The value of the cement mixer depreciated at a constant rate per year. The table below shows the value of the cement mixer after the first and second years: Year 1 2 Value (in dollars) 47,158.35 41,027.76 Which function best represents the value of the cement mixer after t years? f(t) = 47,158.35(0.87)t f(t) = 54,205(0.13)t f(t) = 47,158.35(0.13)t f(t) = 54,205(0.87)t

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  1. Nnesha
    • one year ago
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    1)post a question 2) tag :-)

  2. help_people
    • one year ago
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    |dw:1433768820354:dw|

  3. Nnesha
    • one year ago
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    depreciated meaning what ? any idea how to start ?

  4. Nnesha
    • one year ago
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    key words depreciated constant rate *per* year

  5. help_people
    • one year ago
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    multiply something but no idk where to start

  6. Nnesha
    • one year ago
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    depreciate =decrease

  7. Nnesha
    • one year ago
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    so \[\huge\rm f(t)=P (1- \frac{ r }{ 100 })^t\] r=rate p =starting amount t= years substitute values :-) and then sovle

  8. help_people
    • one year ago
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    where are the vlues?

  9. Nnesha
    • one year ago
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    read the question :-)

  10. help_people
    • one year ago
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    f(t)=54,205(1-r/100)^1?

  11. Nnesha
    • one year ago
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    alright great can you solve for r :-) and yeah when t=1 f(t) = 47158.35 :-)

  12. Nnesha
    • one year ago
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    \[47158.35 =54,205(1-\frac{r}{100})^1\]

  13. help_people
    • one year ago
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    you would diode 54,205 on the other side right

  14. Nnesha
    • one year ago
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    yep divide**

  15. help_people
    • one year ago
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    47185/54205=(1-6/100)^1

  16. help_people
    • one year ago
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    6 is r srry

  17. Nnesha
    • one year ago
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    yep right :-) solve for r

  18. help_people
    • one year ago
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    now I'm confused how to do that can u show me please?

  19. Nnesha
    • one year ago
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    47185/54205= ??

  20. Nnesha
    • one year ago
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    anything to the 1 power equal to same thing so (1-r/100)^1 = 1-r/100

  21. help_people
    • one year ago
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    -1?

  22. Nnesha
    • one year ago
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    nope 47185/54205= ?? divide this first

  23. help_people
    • one year ago
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    ok

  24. help_people
    • one year ago
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    0.87

  25. Nnesha
    • one year ago
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    r isn't .87

  26. Nnesha
    • one year ago
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    did you divide 47185/54205= ??

  27. help_people
    • one year ago
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    yes

  28. Nnesha
    • one year ago
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    show ur work how did you get .87 ?

  29. help_people
    • one year ago
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    on a calc ???

  30. help_people
    • one year ago
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    it was 0.870492

  31. Nnesha
    • one year ago
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    what did you put in to the cal?

  32. help_people
    • one year ago
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    what you exactly told me @Nnesha

  33. Nnesha
    • one year ago
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    \(\color{blue}{\text{Originally Posted by}}\) @help_people 47185/54205=(1-r/100)^1 \(\color{blue}{\text{End of Quote}}\) this is right solve for r i asked a question how did you get .87 and what did you pout into the calculator ? bec i got difference answer for r

  34. Nnesha
    • one year ago
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    put*

  35. help_people
    • one year ago
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    i got .87 by dividing those two numbers like you told me i did not see r equals that @Nnesha

  36. Nnesha
    • one year ago
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    facepalm* i thought u r saying r=.87 >.^

  37. Nnesha
    • one year ago
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    wait we don't have to use that equation mhmm

  38. amistre64
    • one year ago
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    our rate of change from year 1 to year 2 is: \[r=\frac{value_2-value_1}{value_1}\] since we want to know how much worth it has retained, we are interested in 1-r

  39. amistre64
    • one year ago
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    or rather 1 - |r| might be more precise

  40. help_people
    • one year ago
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    so i have to put in the values in r ?

  41. amistre64
    • one year ago
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    you are finding the percentage of difference, yes

  42. help_people
    • one year ago
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    ok

  43. amistre64
    • one year ago
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    for an estimate, what is (47-41)/47?

  44. help_people
    • one year ago
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    0.12766

  45. amistre64
    • one year ago
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    \[\frac{47-41}{47}\implies \frac{47}{47}-\frac{41}{47}\implies 1-\frac{41}{47}\] if you want to see how it relates to Nneshas posts

  46. help_people
    • one year ago
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    round it would be 0.13

  47. amistre64
    • one year ago
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    then we lose about .13 a year we retain about 1-.13

  48. amistre64
    • one year ago
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    what is out value? in other words, how much do we retain as the years go on? which option do you choose now?

  49. help_people
    • one year ago
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    c

  50. amistre64
    • one year ago
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    .13 is NOT what we want ...

  51. amistre64
    • one year ago
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    what is 1 - .13?

  52. amistre64
    • one year ago
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    c tells us how much we have lost over the years. it doesnt really tell us outright what the value is for each year without further calculations.

  53. help_people
    • one year ago
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    then b?

  54. amistre64
    • one year ago
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    does b have .13 in it?

  55. amistre64
    • one year ago
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    do want to have a .13 in it?

  56. amistre64
    • one year ago
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    if we are losing 13% of our value each year, then our value is not 13% if i have 1 dollar, and i have to pay someone 13cents, how much value of that dollar do I have left over?

  57. amistre64
    • one year ago
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    another view of it is 47(.13) = 41 ?

  58. help_people
    • one year ago
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    i don't get it i thought it would be that is tme 13

  59. help_people
    • one year ago
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    @amistre64

  60. amistre64
    • one year ago
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    answer me this ... is 47(1.3) = 41 ? or even close to it?

  61. amistre64
    • one year ago
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    47(.13 ) = 41 that is

  62. amistre64
    • one year ago
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    if .13 is what we lose in value, then how much do we keep in value?

  63. help_people
    • one year ago
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    ? I'm not understudying what ur asking?

  64. amistre64
    • one year ago
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    good luck then, because I really dont have any other way of asking it.

  65. help_people
    • one year ago
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    would we keep .87?

  66. amistre64
    • one year ago
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    yes

  67. help_people
    • one year ago
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    ok then i did understand srry

  68. help_people
    • one year ago
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    so based on that i find a to be the answer

  69. amistre64
    • one year ago
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    'a' is a trick we start with the original value of the equipment

  70. amistre64
    • one year ago
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    54(.87)^0 = 54 , for year 0 its brand new. 54(.87)^1 = 47 or there abouts 54(.87)^2 = 41 or there abouts

  71. help_people
    • one year ago
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    ok

  72. help_people
    • one year ago
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    but remember that equation you gave me earlier about r-value 1-value 2/value1 i used that and found the answer

  73. help_people
    • one year ago
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    so that does nt show the whole information?

  74. amistre64
    • one year ago
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    you found the percent of change from 47 to 41, its a difference calculation. 47 lost 13% to get to 41

  75. amistre64
    • one year ago
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    it shows a method of approaching the solution.

  76. amistre64
    • one year ago
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    41/47 = .87 is valid as well.

  77. help_people
    • one year ago
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    yeah so d? but i still am not getting why

  78. help_people
    • one year ago
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    wait yes i amm srry @amistre64

  79. amistre64
    • one year ago
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    good luck :)

  80. Nnesha
    • one year ago
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    P represents initial amount which is what in the question ?

  81. help_people
    • one year ago
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    thank yo so d is correct ? @amistre64

  82. Nnesha
    • one year ago
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    great explanation amis! you can also use this equation \[47158.35 =54,205(1-\frac{r}{100})^1\] solve for r r=13 plug in \[\large\rm f(t)=54,205(1-\frac{13}{100})^t\] remember p represent initial amount solve the parentheses gO_Od luck! :-)

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