Asked by :3 [SillyAnonymousCat]
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)
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.
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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.
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.
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.
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.
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)
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.
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.
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.
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.
Answers
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Answered by
GPT-5 mini
The first graph: y = 17(0.4)^x + 5.
Reason: horizontal asymptote y = c gives c = 5, and y(0) = a + c = 22 gives a = 17, so y = 17·b^x + 5. To be decreasing for all x, 0 < b < 1 (here b = 0.4).
Reason: horizontal asymptote y = c gives c = 5, and y(0) = a + c = 22 gives a = 17, so y = 17·b^x + 5. To be decreasing for all x, 0 < b < 1 (here b = 0.4).
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