Question
Use the graph to answer the question.
A coordinate plane going from negative 10 to 10 in increments of 1 labeled every 5 units on the x axis and from negative 1 to 15 in increments of 1 labeled every 5 units on the y axis with 2 points labeled at left parenthesis negative 1 comma 10 right parenthesis and at left parenthesis 1 comma 3.6 right parenthesis. A curve is drawn through the 2 points.
Which equation is shown in the graph?
(1 point)
Responses
y=6⋅(0.6)x
y is equal to 6 times 0 point 6 to the x th power
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=10⋅(1.05)x
y is equal to 10 times 1 point 0 5 to the x th power
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A coordinate plane going from negative 10 to 10 in increments of 1 labeled every 5 units on the x axis and from negative 1 to 15 in increments of 1 labeled every 5 units on the y axis with 2 points labeled at left parenthesis negative 1 comma 10 right parenthesis and at left parenthesis 1 comma 3.6 right parenthesis. A curve is drawn through the 2 points.
Which equation is shown in the graph?
(1 point)
Responses
y=6⋅(0.6)x
y is equal to 6 times 0 point 6 to the x th power
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=10⋅(1.05)x
y is equal to 10 times 1 point 0 5 to the x th power
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Answers
GPT-4o mini
To determine which equation is represented by the given points \((-1, 10)\) and \((1, 3.6)\) on the graph, we can evaluate each option by substituting the x-values from the points into the equations and checking if they yield the corresponding y-values.
Let's evaluate each option:
1. **Option 1: \(y = 6 \cdot (0.6)^x\)**
- For \(x = -1\):
\[
y = 6 \cdot (0.6)^{-1} = 6 \cdot \frac{1}{0.6} = 6 \cdot \frac{10}{6} = 10 \quad \text{(correct for } (-1, 10)\text{)}
\]
- For \(x = 1\):
\[
y = 6 \cdot (0.6)^{1} = 6 \cdot 0.6 = 3.6 \quad \text{(correct for } (1, 3.6)\text{)}
\]
2. **Option 2: \(y = 6 \cdot (3.6)^x\)**
- For \(x = -1\):
\[
y = 6 \cdot (3.6)^{-1} = 6 \cdot \frac{1}{3.6} \approx 1.67 \quad \text{(not correct)}
\]
3. **Option 3: \(y = 6 \cdot 0.6x\)**
- This is a linear equation and won't fit the points as is, but let's compute it:
- For \(x = -1\):
\[
y = 6 \cdot 0.6 \cdot (-1) = -3.6 \quad \text{(not correct)}
\]
- For \(x = 1\):
\[
y = 6 \cdot 0.6 \cdot 1 = 3.6 \quad \text{(correct, but doesn't fit both)}
\]
4. **Option 4: \(y = 10 \cdot (1.05)^x\)**
- For \(x = -1\):
\[
y = 10 \cdot (1.05)^{-1} = 10 \cdot \frac{1}{1.05} \approx 9.52 \quad \text{(not correct)}
\]
Based on the evaluations above, only Option 1, \(y = 6 \cdot (0.6)^x\), is consistent with both points provided.
**The correct answer is:** \(y = 6 \cdot (0.6)^x\)
Let's evaluate each option:
1. **Option 1: \(y = 6 \cdot (0.6)^x\)**
- For \(x = -1\):
\[
y = 6 \cdot (0.6)^{-1} = 6 \cdot \frac{1}{0.6} = 6 \cdot \frac{10}{6} = 10 \quad \text{(correct for } (-1, 10)\text{)}
\]
- For \(x = 1\):
\[
y = 6 \cdot (0.6)^{1} = 6 \cdot 0.6 = 3.6 \quad \text{(correct for } (1, 3.6)\text{)}
\]
2. **Option 2: \(y = 6 \cdot (3.6)^x\)**
- For \(x = -1\):
\[
y = 6 \cdot (3.6)^{-1} = 6 \cdot \frac{1}{3.6} \approx 1.67 \quad \text{(not correct)}
\]
3. **Option 3: \(y = 6 \cdot 0.6x\)**
- This is a linear equation and won't fit the points as is, but let's compute it:
- For \(x = -1\):
\[
y = 6 \cdot 0.6 \cdot (-1) = -3.6 \quad \text{(not correct)}
\]
- For \(x = 1\):
\[
y = 6 \cdot 0.6 \cdot 1 = 3.6 \quad \text{(correct, but doesn't fit both)}
\]
4. **Option 4: \(y = 10 \cdot (1.05)^x\)**
- For \(x = -1\):
\[
y = 10 \cdot (1.05)^{-1} = 10 \cdot \frac{1}{1.05} \approx 9.52 \quad \text{(not correct)}
\]
Based on the evaluations above, only Option 1, \(y = 6 \cdot (0.6)^x\), is consistent with both points provided.
**The correct answer is:** \(y = 6 \cdot (0.6)^x\)