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Math Help - Exponential and logarithmic

  1. #1
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    Exponential and logarithmic

    hey, i haven't been for quite a while

    1. If you invest $100 at 2% per day, compounding daily, the amount of money you would have after x days is given by y=100(1.02)^x. For how many days would you have to invest to double your money.

    2. How would you go about sketching 2* 10^(x/10)+4?

    3. y=2^x, y=3^x and y= 5^x
    i. For what of value of x is 2^x > 3^x > 5^x
    ii. For what value of x is 2^x < 3^x < 5^x
    iii. For what value of x is 2^x = 3^x = 5^x

    Thanks
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  2. #2
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    Quote Originally Posted by chaneliman View Post
    hey, i haven't been for quite a while

    1. If you invest $100 at 2% per day, compounding daily, the amount of money you would have after x days is given by y=100(1.02)^x. For how many days would you have to invest to double your money.

    2. How would you go about sketching 2* 10^(x/10)+4?

    3. y=2^x, y=3^x and y= 5^x
    i. For what of value of x is 2^x > 3^x > 5^x
    ii. For what value of x is 2^x < 3^x < 5^x
    iii. For what value of x is 2^x = 3^x = 5^x

    Thanks
    to #1:

    Solve for x:

    200=100 \cdot (1.02)^x (I've got 35 days)

    to #2:

    f(x)=2 \cdot 10^{\frac x{10}}+4 = 2 \left(\sqrt[10]{10} \right)^x+4 with \sqrt[10]{10} \approx 1.2589

    to # 3(iii):

    a^x = b^x~\wedge~b \neq a ~\implies~ x = 0

    (i) x < 0
    (ii) x > 0
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  3. #3
    Bar0n janvdl's Avatar
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    Quote Originally Posted by chaneliman View Post
    hey, i haven't been for quite a while

    1. If you invest $100 at 2% per day, compounding daily, the amount of money you would have after x days is given by y=100(1.02)^x. For how many days would you have to invest to double your money.
    100(1.02)^x = 200

    (1.02)^x = 2

    x = log_{1.02} 2

    x is roughly 35, in other words, 35 days.

    Quote Originally Posted by chaneliman View Post
    2. How would you go about sketching 2* 10^(x/10)+4?
    You are supposed to already know the basic form of an exponential curve.

    Let x = 0
    Then you will find y = 6

    So you know it intersects the y-axis at 6

    We can make 2(10^{\frac{x}{10}}) infinitely small, but not exactly zero.

    So if that part is infinitely small, we have on constant (+ 4) which will be our asymptote. See the attached image for clarification.

    Quote Originally Posted by chaneliman View Post
    3. y=2^x, y=3^x and y= 5^x
    i. For what of value of x is 2^x > 3^x > 5^x
    ii. For what value of x is 2^x < 3^x < 5^x
    iii. For what value of x is 2^x = 3^x = 5^x
    i) Where x < 0
    ii) Where x > 0
    iii) Where x = 0
    Attached Thumbnails Attached Thumbnails Exponential and logarithmic-graph.jpg  
    Last edited by janvdl; April 8th 2008 at 06:13 AM. Reason: My apologies Earboth, I hadn't noticed that you had answered already.
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