Question

xponential Decay Quick Check
5 of 55 of 5 Items























Question
Which graph has the following properties?

The y-intercept is at (0,22)
.
The horizontal asymptote is at y=5
.
The graph is decreasing for all values of x.
(1 point)
Responses

A coordinate plane's x-axis ranges from negative 1 to 6 by 1-unit increments and its y-axis ranges from negative 2 to 30 by 2-unit increments. A solid curve and a dotted line with arrows at both ends are plotted.
▼Click for Long Desc
The solid curve intersects a plotted point on the y-axis located at left parenthesis 0 comma 27 right parenthesis. This curve is labeled y equals 22 multiplied by left parenthesis 0.4 right parenthesis superscript x baseline plus 5. The dotted line is plotted at y equals 5. The solid curve decreases from the marked point to eventually overlap with the dotted line.

Image with description A coordinate plane's x-axis ranges from negative 1 to 6 by 1-unit increments and its y-axis ranges from negative 2 to 30 by 2-unit increments. A solid curve and a dotted line with arrows at both ends are plotted.

A coordinate plane's x-axis ranges from negative 1 to 6 by 1-unit increments and its y-axis ranges from negative 2 to 26 by 2-unit increments. A solid curve and a dotted line with arrows at both ends are plotted.
▼Click for Long Desc
The solid curve passes through a plotted point on the y-axis located at left parenthesis 0 comma 22 right parenthesis. The curve is labeled y equals 22 multiplied by left parenthesis 0.4 right parenthesis superscript x baseline. The dotted line is plotted on the x-axis and horizontally extends from left parenthesis negative 1 comma 0 right parenthesis to left parenthesis 6 comma 0 right parenthesis. The solid curve decreases from the marked point to eventually overlap with the dotted line.

Image with description A coordinate plane's x-axis ranges from negative 1 to 6 by 1-unit increments and its y-axis ranges from negative 2 to 26 by 2-unit increments. A solid curve and a dotted line with arrows at both ends are plotted.

A coordinate plane's x-axis ranges from negative 2 to 6 and its y-axis ranges from negative 2 to 24, both by 2-unit increments. A solid curve and a dotted line with arrows at both ends are plotted. The solid curve intersects a point plotted on the y-axis.
▼Click for Long Desc
The coordinates of the plotted point are left parenthesis 0 comma 22 right parenthesis. The solid curve is labeled y equals 17 multiplied by left parenthesis 0.4 right parenthesis superscript x baseline plus 5. The dotted line is plotted at y equals 7. The solid curve decreases from the marked point, passes through the dotted line, then extends towards y equals 5.

Image with description A coordinate plane's x-axis ranges from negative 2 to 6 and its y-axis ranges from negative 2 to 24, both by 2-unit increments. A solid curve and a dotted line with arrows at both ends are plotted. The solid curve intersects a point plotted on the y-axis.

A coordinate plane's x-axis ranges from negative 6 to 1 by 1-unit increments and its y-axis ranges from negative 2 to 26 by 2-unit increments. A solid curve and a dotted line with arrows at both ends are plotted.
▼Click for Long Desc
The solid curve passes through a plotted point on the y-axis located at left parenthesis 0 comma 22 right parenthesis. The curve is labeled y equals 17 multiplied by left parenthesis 0.4 right parenthesis superscript negative x baseline plus 5. The dotted line is plotted at y equals 5. The solid curve decreases from the marked point to eventually overlap with the dotted line.

Answer 1

The third graph — the one labeled y = 17(0.4)^x + 5.

Reason: at x = 0 y = 17 + 5 = 22 (correct y‑intercept), the horizontal asymptote is y = 5, and the base 0.4 < 1 makes the function decreasing for all x.