Question

Use the image to answer the question.

A coordinate plane's x-axis ranges from negative 1 to 6 and its y-axis ranges from negative 10 to 10, both by 1-unit increments. A solid curve and a dotted line with arrows at both ends are plotted. The solid curve intersects a marked point on the y-axis.
▼Click for Long Desc
The coordinates of the marked point are left parenthesis 0 comma negative 2 right parenthesis. The solid curve is labeled y equals 5 multiplied by left parenthesis 0.3 right parenthesis superscript x baseline minus 7. The dotted line is plotted at y equals negative 7. The solid curve gradually decreases from the marked point to eventually overlap with the dotted line.

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)

The horizontal asymptote is at y=0.3
.

The horizontal asymptote is at y=5
.

The horizontal asymptote is at y=0
.

The horizontal asymptote is at y=−7
.

Answer 1

The horizontal asymptote is y = −7.

Reason: as x → ∞, (0.3)^x → 0, so y = 5(0.3)^x − 7 → −7 (the curve approaches the dotted line y = −7).