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anonymous

  • one year ago

Medal and FAN John has taken out a loan for college. He started paying off the loan with a first payment of $100. Each month he pays, he wants to pay back 1.1 times as the amount he paid the month before. . Explain why this series is convergent or divergent

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  1. anonymous
    • one year ago
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    just tell me is this convergent or divergent

  2. SolomonZelman
    • one year ago
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    well, just paying 1.1 times the previous payment means that sequence diverges (nothing to even talk about a series). BUT, a loan (I would think so) is some finite amount though, so this situtation with a loan is a bad example.....

  3. SolomonZelman
    • one year ago
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    he won't go into paying more than the loan...... (and this all I am assuming there is no interest, since it is not mentioned here)

  4. SolomonZelman
    • one year ago
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    So, lets write this series, and lets diregard the fact that he is to pay some finite loan amount. OK?

  5. anonymous
    • one year ago
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    is an infinite series that is not convergent, meaning that the infinite sequence of the partial sums of the series does not have a finite limit.

  6. anonymous
    • one year ago
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    is divergent

  7. SolomonZelman
    • one year ago
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    \(\large\color{black}{ \displaystyle a_1=100 }\) \(\large\color{black}{ \displaystyle r=1.1 }\) and this is a perfect geometric series. For geometric series to converge, normally, the folloing mst be true: `|r|<1` yes correct (disregarding the fact that it's a loan).

  8. SolomonZelman
    • one year ago
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    The fact that it is a loan is forcing a FINITE series.

  9. SolomonZelman
    • one year ago
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    If you were to propose a different scenario, such as:

  10. SolomonZelman
    • one year ago
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    John is giving a charity to poor children who stand by the Church. THe first month he gave 100$ and then, every month, he wants to give 1.1 times as much as he gave the previous month. is this series convergent or divergent?

  11. SolomonZelman
    • one year ago
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    this would be more like an INFINITE series scenraio....

  12. anonymous
    • one year ago
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    ok thanks can u help with another question

  13. SolomonZelman
    • one year ago
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    ok, but what course is this?

  14. SolomonZelman
    • one year ago
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    is this geometry or calc?

  15. anonymous
    • one year ago
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    algebra 2

  16. SolomonZelman
    • one year ago
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    oh, i see.... go ahead...

  17. SolomonZelman
    • one year ago
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    ((in calc there are more advanced "tools" to use))

  18. anonymous
    • one year ago
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    The graph of f(x) = 2^x + 1 is shown below. Explain how to find the average rate of change between x = 0 and x = 3

  19. SolomonZelman
    • one year ago
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    find f(0). find f(3). find the slope between (0,f(0)) and (3,f(3)).

  20. SolomonZelman
    • one year ago
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    making sense?

  21. anonymous
    • one year ago
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  22. anonymous
    • one year ago
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    thats the graph

  23. SolomonZelman
    • one year ago
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    no need for a graph to perform this task, but, it is nice to have one.

  24. SolomonZelman
    • one year ago
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    do my steps to the solution make sense?

  25. anonymous
    • one year ago
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    no

  26. SolomonZelman
    • one year ago
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    Ok, lets do it togther one by one.

  27. anonymous
    • one year ago
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    so basically your finding slope

  28. SolomonZelman
    • one year ago
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    yes

  29. SolomonZelman
    • one year ago
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    did you find f(0) and f(3) ?

  30. SolomonZelman
    • one year ago
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    f(x) = 2\(^x\)+1

  31. SolomonZelman
    • one year ago
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    f(0)=2\(^0\)+1=? f(3)=2\(^3\)+1=?

  32. anonymous
    • one year ago
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    f(3) =7

  33. SolomonZelman
    • one year ago
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    close

  34. SolomonZelman
    • one year ago
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    2³ = ?

  35. anonymous
    • one year ago
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    9

  36. anonymous
    • one year ago
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    oops

  37. SolomonZelman
    • one year ago
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    9 is f(3) or just the 2³ part?

  38. anonymous
    • one year ago
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    2^3

  39. SolomonZelman
    • one year ago
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    \(2^3=2\times 2 \times 2 \)

  40. SolomonZelman
    • one year ago
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    =8

  41. anonymous
    • one year ago
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    f(0) = 1

  42. anonymous
    • one year ago
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    f(3) = 9

  43. anonymous
    • one year ago
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    i meant that

  44. SolomonZelman
    • one year ago
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    yes,

  45. SolomonZelman
    • one year ago
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    f(3)=9

  46. SolomonZelman
    • one year ago
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    and f(0)=?

  47. anonymous
    • one year ago
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    1

  48. SolomonZelman
    • one year ago
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    no

  49. SolomonZelman
    • one year ago
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    your function is \(f(x)=2^x+1\)

  50. SolomonZelman
    • one year ago
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    \(f(0)=2^0+1=?\)

  51. anonymous
    • one year ago
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    f(0) = 0 + 1

  52. SolomonZelman
    • one year ago
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    \({\rm C}^0=1\) (for any real number C)

  53. anonymous
    • one year ago
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    f(0) = 1

  54. SolomonZelman
    • one year ago
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    \( f(0)=2^0+1=1+1=?\)

  55. anonymous
    • one year ago
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    2

  56. SolomonZelman
    • one year ago
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    yes, f(0)=2

  57. anonymous
    • one year ago
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    Explain how to find the average rate of change between x = 0 and x = 3.

  58. SolomonZelman
    • one year ago
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    now, you need to find the slope between (0,f(0)) and (3,f(3)). we know f(3)=9, f(0)=2. SO lets plug this in. ~ you have to find the slope between (0,2) and (3,9)

  59. SolomonZelman
    • one year ago
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    \(\LARGE \color{black}{ \displaystyle {\rm m}=\frac{\color{blue}{{\rm y}_1}-\color{red}{{\rm y}_2}}{\color{green}{{\rm x}_1}-\color{darkgoldenrod}{{\rm x}_2}} }\) where \(\LARGE \color{black}{ \displaystyle {\rm m} }\) is the slope \(\Large\color{black}{ \displaystyle (\color{green}{{\rm x}_1}~,~~\color{blue}{{\rm y}_1}) }\) and \(\Large\color{black}{ \displaystyle (\color{darkgoldenrod}{{\rm x}_2}~,~~\color{red}{{\rm y}_2}) }\) are your two points.

  60. anonymous
    • one year ago
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    9-2 =7 3-0 =3

  61. SolomonZelman
    • one year ago
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    yes, so your slope is?

  62. anonymous
    • one year ago
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    7/3

  63. SolomonZelman
    • one year ago
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    yup

  64. anonymous
    • one year ago
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    is that the final answer

  65. SolomonZelman
    • one year ago
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    yes, that is the final answer for your second question.

  66. anonymous
    • one year ago
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    so what is the average rate of change again

  67. SolomonZelman
    • one year ago
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    7/3 :)

  68. SolomonZelman
    • one year ago
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    slope and average rate of change (in this context) is the same thing.

  69. anonymous
    • one year ago
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    thanks so much

  70. SolomonZelman
    • one year ago
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    you are welcome !

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