Results 1 to 2 of 2
Like Tree1Thanks
  • 1 Post By Debsta

Thread: What would the "starting amount" be in these functions?

  1. #1
    Junior Member
    Joined
    Dec 2018
    From
    USA
    Posts
    29
    Thanks
    2

    What would the "starting amount" be in these functions?

    Here are two functions: (they resemble growth and decay functions)

    f(x) = 2*(1/8)^x and h(x) = -7*(1.567)^x-5

    I heard that the first digit is the starting amount, such as 2 in f(x) and -7 in h(x).

    This is proven wrong when I input h(0) into the second function. The reason I input 0 is because it is logically the starting amount of x, but this assumption immediately contradicts h(x)'s starting amount of "-7" if solved for x=0. The answer? -0.74.

    Which claim should I follow? The "first-digit-is-the-starting-amount," claim or my "zero-is-the-logical-start-point," claim?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    From
    Brisbane
    Posts
    1,223
    Thanks
    449

    Re: What would the "starting amount" be in these functions?

    Quote Originally Posted by bossbasslol View Post
    Here are two functions: (they resemble growth and decay functions)

    f(x) = 2*(1/8)^x and h(x) = -7*(1.567)^x-5

    I heard that the first digit is the starting amount, such as 2 in f(x) and -7 in h(x).

    This is proven wrong when I input h(0) into the second function. The reason I input 0 is because it is logically the starting amount of x, but this assumption immediately contradicts h(x)'s starting amount of "-7" if solved for x=0. The answer? -0.74.

    Which claim should I follow? The "first-digit-is-the-starting-amount," claim or my "zero-is-the-logical-start-point," claim?

    "The first digit is the starting amount" claim only works when the exponent is x (or a multiple of x) as in f(x)=2*(1/8)^x. When you substitute in x=0, you get 2*(1/8)^0 = 2*1 = 2.
    The reason you get the starting digit is because (1/8)^0 =1 (anything raised to the power of 0 is equal to 1 (except 0 itself)) and so you are left with the 2.

    But if the power is x-5 as in g(x), you won't get that 1 (when you substitute x=0) to leave you with "the first digit".

    Don't learn a "rule" if you don't understand it. Always put in x=0 for "starting value" (ie if x is representing time).
    Thanks from bossbasslol
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: Dec 1st 2015, 05:34 PM
  2. Replies: 2
    Last Post: Apr 2nd 2012, 07:06 PM
  3. Replies: 2
    Last Post: Jun 4th 2011, 12:11 PM
  4. Replies: 2
    Last Post: Apr 24th 2011, 07:01 AM
  5. Replies: 1
    Last Post: Oct 25th 2010, 04:45 AM

/mathhelpforum @mathhelpforum