Question

Use the graph of the exponential decay function that models an exponential decay sequence to discuss the properties and determine the equation for the horizontal asymptote of the graph.

(1 point)
Responses

The horizontal asymptote is at y=−7
.
The horizontal asymptote is at y equals negative 7 .

The horizontal asymptote is at y=0.3
.
The horizontal asymptote is at y equals 0.3 .

The horizontal asymptote is at y=0
.
The horizontal asymptote is at y equals 0 .

The horizontal asymptote is at y=5
.

Answer 1

The horizontal asymptote is y = 0.

Reason: for a (non-shifted) exponential decay f(x) = a·b^x with 0 < b < 1, as x → ∞ the term b^x → 0 so f(x) → 0, giving the horizontal asymptote y = 0.