How can you tell from an exponential equation if it’s a growth or decay model?

How can you tell from an exponential equation if it's a growth or decay model?

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  1. A growth equation will have a base that is equal to or greater than 1.

    f(x)=2* [tex]5^{x}[/tex] is a growth equation because 2 is greater than 1.

    f(x)=.24*[tex]5^{x}[/tex] is a decay equation because .24 is less than 1.

    Step-by-step explanation:

  2. ok we know that exponential functions have exponent at the top the funtions.

    the general form of exponential function is [tex]f(x)=y=a^x[/tex].

    we know that x is the exponent here.

    if we have positive value of x .

    we can say that exponential function is increasing or growth function.

    if we have negative value of x it is decreasing or decay.

    exponential function for decay is [tex]f(x)=y=a^-x[/tex].

    where x is decreasing in decay function.

  3. But sometimes things can grow (or the opposite: decay) exponentially, at least for a while.

    So we have a generally useful formula:

    y(t) = a × ekt

    Where y(t) = value at time "t"
    a = value at the start
    k = rate of growth (when >0) or decay (when <0)
    t = time

  4. Step-by-step explanation:

    The general form of an exponential equation for growth is


    and for decay is


    In general, if the number inside the parenthesis (the growth or decay rate) is greater than 1, it's a growth problem.  If the number inside the parenthesis is greater than 0 but less than 1 (in other words a positive fraction), it's a decay problem.

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