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Math Help - 2 "constants" + 2 variable question

  1. #1
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    2 "constants" + 2 variable question

    Hi, I'm not sure how I can solve this question.

    y = k(a^x)

    Given: whenever the value of x is increased by 3, the value of y is doubled. Also 'k' and 'a' are positive constants.

    I need to determine the value of k and a. The question allows for them to be indeterminable.

    I'd like to start by making some relation between x and y but I'm not sure if that's what I should do. Something like this:

    2x = y + 3

    But I don't know if doing that makes any sense, since they don't actually equal each other for most values of x and y...

    From there I would've liked to move that equation around to isolate y and substitute that into the original equation. However that still leaves 3 variables. I've tried to re-arrange the equation to isolate a or k, but when I try to put in answer on the web-form it complains that 'k' is undefined for example. So it would seem I have to somehow find concrete numbers for a and k but I have no idea how...
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  2. #2
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    Quote Originally Posted by cb220 View Post
    Hi, I'm not sure how I can solve this question.

    y = k(a^x)

    Given: whenever the value of x is increased by 3, the value of y is doubled. Also 'k' and 'a' are positive constants.
    Think about it like this

    when x=0, then y=k

    when x=3, then y= 2k

    when x=6, then y= 2(2k) = 4k

    when x=9, then y= 2(4k) = 8k
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  3. #3
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    Quote Originally Posted by cb220 View Post
    Hi, I'm not sure how I can solve this question.

    y = k(a^x)

    Given: whenever the value of x is increased by 3, the value of y is doubled. Also 'k' and 'a' are positive constants.

    I need to determine the value of k and a. The question allows for them to be indeterminable.

    I'd like to start by making some relation between x and y but I'm not sure if that's what I should do. Something like this:

    2x = y + 3

    But I don't know if doing that makes any sense, since they don't actually equal each other for most values of x and y...

    From there I would've liked to move that equation around to isolate y and substitute that into the original equation. However that still leaves 3 variables. I've tried to re-arrange the equation to isolate a or k, but when I try to put in answer on the web-form it complains that 'k' is undefined for example. So it would seem I have to somehow find concrete numbers for a and k but I have no idea how...
    Maybe simplest is

    y=ka^x

    2y=ka^{x+3}=ka^xa^3

    2y=ya^3

    which gives a value for a^3 to start.
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  4. #4
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    Thanks for the quick replies!

    Hmm, wow I don't think I would've thought to do it like that if I looked at it for a hundred years heh. But it makes sense now that I see it. Thanks!
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