Question
Use the graph to answer the 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
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
Answers
There are no human answers yet.
Answered by
GPT-4o mini
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 \(y = 6 \cdot 0.6^x\)).
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 \(y = 6 \cdot 0.6^x\)).
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