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swiftskier96

How do you solve this?? N = 3,500e^(k * 9.5)

  • one year ago
  • one year ago

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  1. swiftskier96
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    How do you solve this?? N = 3,500e^(k * 9.5)

    • one year ago
  2. CalebBeavers
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    There's two variables...

    • one year ago
  3. swiftskier96
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    I know. Im supposed to solve for k. Does that help at least a little bit? @CalebBeavers

    • one year ago
  4. CalebBeavers
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    Hmm, start off by dividing both sides by 3500

    • one year ago
  5. swiftskier96
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    So it would be N/3,500 = e^9.5k? @CalebBeavers

    • one year ago
  6. CalebBeavers
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    Yeah, now take natural log of both sides

    • one year ago
  7. swiftskier96
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    So In(N/3,500) = 9.5k?

    • one year ago
  8. CalebBeavers
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    Yep, now just divide by 9.5

    • one year ago
  9. swiftskier96
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    So In(N/3,500)/9.5 = k?

    • one year ago
  10. CalebBeavers
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    Yep =D

    • one year ago
  11. swiftskier96
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    But the questions says to Use the function to find the value of the boat after 9.5 years. (Not this question, the question on my assignment.) Is that the boat value?

    • one year ago
  12. CalebBeavers
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    so it gives you the function N = 3,500e^(kt) ?

    • one year ago
  13. swiftskier96
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    Well it didnt give me that but i asked the question earlier and someone said to use that equation.

    • one year ago
  14. CalebBeavers
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    Hmmm. lets start over whats the original question and all the information it gives you?

    • one year ago
  15. 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. @CalebBeavers

    • one year ago
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  16. CalebBeavers
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    Hmm so \[\large f(t)=ae^{kt}\] use known information from the graph, say point (3,1500) the a is the value at the start so plug these in and solve for k \[1500=3500e^{3k}\] when you know k you can plug it back in to solve for the value at 9.5 years

    • one year ago
  17. swiftskier96
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    So if i plugged in 9.5 it would look like 1500 = 3500e^(3 * 9.5)?

    • one year ago
  18. CalebBeavers
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    No, we need to solve for k. t represents time, we know after 3 years it was 1500 so were plugging that in so we have one variable to solve for

    • one year ago
  19. swiftskier96
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    We need to solve for e?

    • one year ago
  20. CalebBeavers
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    e is eulers number, its a constant just solve for k in \[\large1500=3500e^{3k}\]

    • one year ago
  21. swiftskier96
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    Oh ok. So i would have to divide each side by 3500 right? That would give me 3/7 = e^3k. Then take the inverse of each side which would give me In(3/7) = 3k right?

    • one year ago
  22. CalebBeavers
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    Yep, now divide by 3

    • one year ago
  23. CalebBeavers
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    ln(3/7)/3=k now you know k, plug it back in along with the time you want to know which is 9.5 \[f(t)=3500e^{(\ln(3/7)/3)9.5}\]

    • one year ago
  24. swiftskier96
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    So is that my final answer? Or do i have to solve more of it?

    • one year ago
  25. swiftskier96
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    @CalebBeavers

    • one year ago
  26. swiftskier96
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    @CalebBeavers I dont want to bug you, but i have to log off soon and i really need to know if thats my final answer or what more i have to do.

    • one year ago
  27. CalebBeavers
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    My bad, i didnt even see the notification. if you plug the right hand side into a calculator it will give you the value of the boat after 9.5 years

    • one year ago
  28. swiftskier96
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    I did 3/7 = 0.42857142857142857142857142857143 then divided that by 3 and that equaled 0.14285714285714285714285714285714. Then i multiplied it by 9.5 and got 1.3571428571428571428571428571429. Then i pressed the In button and got 0.3053816495511818454864425669865. Is that right? Oh wait! Then do i do 3500e? The only thing is i dont see an e button on my calculator.

    • one year ago
  29. CalebBeavers
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    You should plug it all in at once. use this calculator and type it in like 3500e^((ln(3/7)/3)*9.5)) http://web2.0calc.com/

    • one year ago
  30. swiftskier96
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    Im trying but its being stupid. Either that or im stupid. I typed it all in and it wont let me press the = sign. When i do press it, it wont solve it.

    • one year ago
  31. CalebBeavers
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    Well it gives me 239.226

    • one year ago
  32. swiftskier96
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    Ok. Sorry. My computers stupid... lol Thanks for the help and being super patient!!!

    • one year ago
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