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Math Help - Need help with a AB Problem!

  1. #1
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    Need help with a AB Problem!

    Dear all, I am a high school student & I have the following problem which to me it is very confusing.



    Thank you very much!
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by mak15 View Post
    Dear all, I am a high school student & I have the following problem which to me it is very confusing.



    Thank you very much!
    (a) this is a separable differential equation.

    you want to solve R' = kR

    rewrite as \frac {R'}R = k

    now integrate both sides and continue (don't forget the arbitrary constant). use the clues given in the question to solve for the unknown.


    (b) once you answered part (a), plug in R = 10 and solve for t


    (c) kt_h = \ln 2, always

    here t_h is the half-life, k is the rate of decay.
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  3. #3
    Behold, the power of SARDINES!
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    \frac{dR}{dt}=kR \iff \frac{dR}{r}=kdt so integrate both sides

    \int \frac{dR}{R}= \int kdt \iff ln(R)=kt+c

    solveing for R

    R=e^{kt+c}=e^{kt} \cdot e^c=Ae^{kt}

    R(t)=Ae^{kt}

    R(0)=10^6=Ae^{0}


    You should be able to finish from here.

    Good luck.
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  4. #4
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    Quote Originally Posted by TheEmptySet View Post
    \frac{dR}{dt}=kR \iff \frac{dR}{r}=kdt so integrate both sides

    \int \frac{dR}{R}= \int kdt \iff ln(R)=kt+c

    solveing for R

    R=e^{kt+c}=e^{kt} \cdot e^c=Ae^{kt}

    R(t)=Ae^{kt}

    R(0)=10^6=Ae^{0}


    You should be able to finish from here.

    Good luck.
    Thank you so much for ALL of your replies!
    I understand the A is a constant and I got A = 1,000,000
    But I am not sure about Part C, Half-Life?
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  5. #5
    Behold, the power of SARDINES!
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    Quote Originally Posted by mak15 View Post
    Thank you so much for ALL of your replies!
    I understand the A is a constant and I got A = 1,000,000
    But I am not sure about Part C, Half-Life?

    Solve the equation

    \frac{1000000}{2}=1000000e^{kt}

    using the value of k you got from part A.

    Good luck.
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  6. #6
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    Quote Originally Posted by TheEmptySet View Post
    Solve the equation

    \frac{1000000}{2}=1000000e^{kt}

    using the value of k you got from part A.

    Good luck.
    Thank you very much to you all! I think I got it!
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