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Math Help - Did I integrate these properly?

  1. #1
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    Did I integrate these properly?

    I have this question:

    1. The amount a fish grows follows the differential equation
    dL/dt = 6.48e^-0.09t,


    with initial condition L(0) = 5, where t is measured in years and L is measured in centimetres. How much does the fish grow between ages t = 0.5 and t = 1.5?



    (Give your answer to two decimal places.)



    I integrated it to L(t) = -72e^-0.09t and did the definite integral calculation getting ~6cm. However, when I sub in L(0), I don't get 5. Is that relevant?
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  2. #2
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    I bet you forgot your integration constant?.

    L=-72e^{-\frac{9t}{100}}+C

    5=-72+C

    C=77

    L=-72e^{\frac{-9t}{100}}+77

    Now, try your t=.5 and t=1.5
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  3. #3
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    *facepalms*

    D'OH!

    thank you
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  4. #4
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    Quote Originally Posted by jschlarb View Post
    I have this question:

    1. The amount a fish grows follows the differential equation
    dL/dt = 6.48e^-0.09t,


    with initial condition L(0) = 5, where t is measured in years and L is measured in centimetres. How much does the fish grow between ages t = 0.5 and t = 1.5?



    (Give your answer to two decimal places.)



    I integrated it to L(t) = -72e^-0.09t and did the definite integral calculation getting ~6cm. However, when I sub in L(0), I don't get 5. Is that relevant?
    You are correct apart from missing out the constant of integration (that alters your answer so that L(0) = 5). But if you did a definite integral with the limits, this is not necessary anyway, and indeed the change in length is around 6.
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