Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

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

at and a y-intercept of 4.

Relevance
• 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.

:)>

• ?
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

• 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?