Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

PLEASE HELPP!!!!!!?

6. Determine the equation in the form of a decreasing exponential function with an asymptote

at and a y-intercept of 4.

3 Answers

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  • 2 months ago

    An decreasing exponential function could be of the form:

    f(x) = a.b⁻ˣ​​​ + c

    so, when x = 0 we have:

    f(0) = a + c => 4

    Hence, a could be 3 and c could be 1

    i.e. f(x) = 3b⁻ˣ​​​ + 1

    Choosing, say b = 2 we have:

    f(x) = 3(2)⁻ˣ​​​ + 1

    Note: as x --> ∞, 3(2)⁻ˣ --> 0

    Hence, f(x) --> 1....i.e. horizontal asymptote

    A sketch is below.

    :)>

     

    Attachment image
  • ?
    Lv 7
    2 months ago

    Your post is not clear. You want a decreasing exponential function "with an asymptote at" ???? WHAT??? and a y-intercept of 4.

    The following function(s) will satisfy your post:

    h(x) = 2⁻ˣ + 3

    f(x) = a⁻ˣ + 3 where a > 0

    g(x) = aᵇˣ + 3 where a > 0 and b < 0

    Attachment image
  • rotchm
    Lv 7
    2 months ago

    Hints: Unanon yourself and you will get more responses. Its impolite to be anon and people tend to avoid them. 

    General form y = A*b^(-x). The y intercept is when x = 0. And your y is then to be 4. Conclusion?

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