6. Determine the equation in the form of a decreasing exponential function with an asymptote
at and a y-intercept of 4.
- Wayne DeguManLv 74 weeks 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.
- ?Lv 74 weeks 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
- rotchmLv 74 weeks 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?