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vera_ewing

  • one year ago

The temperature of a chemical reaction ranges between 30°C and 70°C. The temperature is at its lowest point when t = 0 and completes one cycle over a six-hour period. What is a sine function that would model this reaction?

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  1. vera_ewing
    • one year ago
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    @Michele_Laino f(t) = 50 sin 10t + 20 ?

  2. Michele_Laino
    • one year ago
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    the amplitude of your function, is: \[\Large A = \frac{{\max value - \min value}}{2} = \frac{{70 - 30}}{2} = ...?\]

  3. vera_ewing
    • one year ago
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    40/2 = 20

  4. vera_ewing
    • one year ago
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    f(t) = 20 sin 10t + 50 is the answer?

  5. Michele_Laino
    • one year ago
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    we can write: \[\Large f\left( t \right) = 20\sin \left( {Bt} \right) + 50\] since we have these limit values: \[\Large 30 \leqslant 20\sin \left( {Bt} \right) + 50 \leqslant 70\]

  6. Michele_Laino
    • one year ago
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    now we have to determine the value of the constant B

  7. vera_ewing
    • one year ago
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    So it's f(t) = 20 sin pi/5 t + 50 ?

  8. Michele_Laino
    • one year ago
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    I think that we have: \[\Large B = \frac{{2\pi }}{6}\] since our function has to assume the same values after 6 hours

  9. Michele_Laino
    • one year ago
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    therefore: \[\Large f\left( t \right) = 20\sin \left( {\frac{{2\pi }}{6}t} \right) + 50\] is the right function

  10. vera_ewing
    • one year ago
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  11. vera_ewing
    • one year ago
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    Those are my answer choices ^

  12. Michele_Laino
    • one year ago
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    please wait a moment, I'm pondering...

  13. Michele_Laino
    • one year ago
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    please look at this drawing:

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  14. Michele_Laino
    • one year ago
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    maybe there is a typo since we can rewrite our function as below: \[\Large f\left( t \right) = 20\sin \left( {\frac{\pi }{3}t} \right) + 50\]

  15. Michele_Laino
    • one year ago
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    please wait a moment, I understand

  16. Michele_Laino
    • one year ago
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    I confirm my answer above

  17. vera_ewing
    • one year ago
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    So which one should I choose?

  18. Michele_Laino
    • one year ago
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    try with the last option, please

  19. Michele_Laino
    • one year ago
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    is the period T=10 hours?

  20. Michele_Laino
    • one year ago
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    I think that there is a typo, namely: T=10 hours and not T=6 hours

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