Answer:
(1, 1.6)
(0, 8)
Step-by-step explanation:
Given exponential function:
[tex]f(x)=8\left(\dfrac{1}{5}\right)^x[/tex]
Given ordered pairs:
- (-2, 80)
- (1, 1.6)
- (0, 8)
- (-1, -40)
To determine which of the given ordered pairs lie on the graph of the given exponential function, substitute each x-coordinate into the function and compare the y-coordinate.
[tex]\begin{aligned}x=-2 \implies y&=8\left(\dfrac{1}{5}\right)^{-2}\\&=8(25)\\&=200\end{aligned}[/tex]
As (-2, 200) ≠ (-2, 80) the ordered pair (-2, 80) does not lie on the graph.
[tex]\begin{aligned}x=1 \implies y&=8\left(\dfrac{1}{5}\right)^{1}\\&=8\left(\dfrac{1}{5}\right)\\&=1.6\end{aligned}[/tex]
As (1, 1.6) = (1, 1.6) the ordered pair (1, 1.6) does lie on the graph.
[tex]\begin{aligned}x=0 \implies y&=8\left(\dfrac{1}{5}\right)^{0}\\&=8(1)\\&=8\end{aligned}[/tex]
As (0, 8) = (0, 8) the ordered pair (0, 8) does lie on the graph.
[tex]\begin{aligned}x=-1 \implies y&=8\left(\dfrac{1}{5}\right)^{-1}\\&=8(5)\\&=40\end{aligned}[/tex]
As (-1, 40) ≠ (-1, -40) the ordered pair (-1, -40) does not lie on the graph.
