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Math Help - Economics consumption spending.

  1. #1
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    Economics consumption spending.

    I had this question in a test and had no idea how to answer it.


    The function  C = 500(1-e^{-0.3x}) shows individual consumption spending (C) in $ as a function of income (x) in $000. At what income level will and individual have consumption spending of $400? You may find it helpful to use the fact that ln0.2 =-1.609 to 3dp.

    Could someone please walk me through how i work these questions out , they really stump me.

    Thanks.
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  2. #2
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    Quote Originally Posted by el123 View Post
    I had this question in a test and had no idea how to answer it.


    The function  C = 500(1-e^{-0.3x}) shows individual consumption spending (C) in $ as a function of income (x) in $000. At what income level will and individual have consumption spending of $400? You may find it helpful to use the fact that ln0.2 =-1.609 to 3dp.

    Could someone please walk me through how i work these questions out , they really stump me.

    Thanks.
    Solve  400 = 500(1-e^{-0.3x}) for x. Then multiply x by 1000.
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    ok so so far i have got

      400 = 500(1-e^{-0.3x})

      400=500-500e^{-0.3x}

     400 + 500e^{-0.3x} = 500

     500e^{-0.3x} = 500-400

     \frac{500e^{-0.3x}}{500}=\frac{100}{500}

     e^{-0.3x} = \frac{1}{5}

    Thats where i get stuck , i don't know how to deal with the e. Get's me every time.
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  4. #4
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    ok so i tried this is this correct?

    x=\frac{\ln{\frac{1}{5}} }{-0.3}
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  5. #5
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    Quote Originally Posted by el123 View Post
    ok so i tried this is this correct?

    x=\frac{\ln{\frac{1}{5}} }{-0.3}
    Correct. And you're told that ln0.2 =-1.609 ....
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