Use the graph to answer the question.

Question

image shows y axis 15 down to 0 and x axis -10 to 10. points -1, 10 and 1, 3.6 are shown

Which equation is shown in the graph? (1 point) Responses y=6⋅(3.6)x y is equal to 6 times 3 point 6 to the x th power y=6⋅0.6x y is equal to 6 times 0 point 6 x y=6⋅(0.6)x y is equal to 6 times 0 point 6 to the x th power y=10⋅(1.05)x

Answer 1

To determine which equation corresponds to the points shown on the graph, we can analyze the provided points (-1, 10) and (1, 3.6).

First, let's check them against the proposed equations.

1. For $y=6\cdot (3.6{)}^x$:
   • When $x=-1$: $y=6\cdot (3.6{)}^{-1}=6/3.6\approx 1.67$ (not a match for $y=10$)
   • When $x=1$: $y=6\cdot (3.6{)}^1=21.6$ (not a match for $y=3.6$)

This equation does not fit.

2. For $y=6\cdot (0.6{)}^x$:
   • When $x=-1$: $y=6\cdot (0.6{)}^{-1}=6/0.6=10$ (matches!)
   • When $x=1$: $y=6\cdot (0.6{)}^1=6\cdot 0.6=3.6$ (matches!)

This equation fits both points.

3. For $y=10\cdot (1.05{)}^x$:
   • When $x=-1$: $y=10\cdot (1.05{)}^{-1}\approx 9.52$ (not a match for $y=10$)
   • When $x=1$: $y=10\cdot (1.05{)}^1=10.5$ (not a match for $y=3.6$)

This equation does not fit.

4. For $y=6\cdot {0.6}^x$ is essentially the same as the third equation expressed differently, so it will yield the same results as the previously evaluated $y=6\cdot (0.6{)}^x$, confirming the match for both points as well.

Based on this analysis, the appropriate equation shown in the graph is $y=6\cdot (0.6{)}^x$ (which can also be referred to as $y=6\cdot {0.6}^x$).