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.



A. 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.

B. 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.

C. 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.

D. 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.

Answer 1

D

Reason: For y = A·b^x + 5 to have y-intercept 22 we need A + 5 = 22 ⇒ A = 17. To be decreasing for all x we need 0 < b < 1 (ln b < 0), so b = 0.4 fits. That gives y = 17(0.4)^x + 5, which matches choice D.