Question

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 = 0.

The horizontal asymptote is at y = 5.

The horizontal asymptote is at y = -7.

Answer 1

y = -7

Reason: y = 5(0.3)^x − 7. As x → ∞, (0.3)^x → 0, so y → −7; hence the horizontal asymptote is y = −7.