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swiftskier96

Help!?!?!?!?!?!? 14. The exponential decay graph shows the expected depreciation for a new boat, selling for $3500, over 10 years. Write an exponential function for the graph. Use the function to find the value of the boat after 9.5 years. Show your work.

  • one year ago
  • one year ago

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  1. swiftskier96
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    14. The exponential decay graph shows the expected depreciation for a new boat, selling for $3500, over 10 years. Write an exponential function for the graph. Use the function to find the value of the boat after 9.5 years. Show your work.

    • one year ago
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  2. binarymimic
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    oh. well the initial value is 3500 and it looks like at t = 2 the value is 2000 try setting up a general exponential function like \[N = N _{0}e^{kt}\]

    • one year ago
  3. binarymimic
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    where N0 is the initial value, N is the present value, k is a constant, and t is the time

    • one year ago
  4. swiftskier96
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    So the initial value would be 3500, the present value is 2000, im not sure what k is, and t is 9.5 years? @binarymimic

    • one year ago
  5. swiftskier96
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    What is k? @binarymimic

    • one year ago
  6. binarymimic
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    you'd have to solve for it by letting N0 = 3500, N = 2000, and t = 2

    • one year ago
  7. binarymimic
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    because at t = 2, the present value is 2000 hence 2000 = 3500e^(k*2) when you get a value for k it will be negative, and try to round it to at least 5 digits for accuracy

    • one year ago
  8. swiftskier96
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    Ohhh ok. I see. Thank you! :)

    • one year ago
  9. binarymimic
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    sure. and when you get the value of k then you can write out the general equation and let t = 9.5

    • one year ago
  10. swiftskier96
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    Then do i add the answers together or something? Cause then ill have k = ? and k = ?.

    • one year ago
  11. binarymimic
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    not sure what you mean but when you solve for k, then you'll use that k in the equation \[N = 3500e ^{k * 9.5}\] to solve for the present value at time t = 9.5

    • one year ago
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