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.
the two marked points are -1, 10 and 1, 3.6
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⋅(0.6)x
y is equal to 6 times 0 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
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.
the two marked points are -1, 10 and 1, 3.6
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⋅(0.6)x
y is equal to 6 times 0 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
Answers
GPT-4o mini
To determine which equation fits the points \((-1, 10)\) and \( (1, 3.6)\), we can test each provided equation.
1. **Equation: \(y = 6 \cdot (3.6)^x\)**
- For \(x = -1\):
\(y = 6 \cdot (3.6)^{-1} = 6 \cdot \frac{1}{3.6} = \frac{6}{3.6} = 1.67\) (not 10)
- For \(x = 1\):
\(y = 6 \cdot (3.6)^{1} = 6 \cdot 3.6 = 21.6\) (not 3.6)
2. **Equation: \(y = 6 \cdot (0.6)^x\)**
- For \(x = -1\):
\(y = 6 \cdot (0.6)^{-1} = 6 \cdot \frac{1}{0.6} = 10\) (correct)
- For \(x = 1\):
\(y = 6 \cdot (0.6)^{1} = 6 \cdot 0.6 = 3.6\) (correct)
3. **Equation: \(y = 6 \cdot 0.6x\)**
- For \(x = -1\):
\(y = 6 \cdot 0.6 \cdot -1 = -3.6\) (not 10)
- For \(x = 1\):
\(y = 6 \cdot 0.6 \cdot 1 = 3.6\) (correct)
4. **Equation: \(y = 10 \cdot (1.05)^x\)**
- For \(x = -1\):
\(y = 10 \cdot (1.05)^{-1} = 10 \cdot \frac{1}{1.05} \approx 9.52\) (not 10)
- For \(x = 1\):
\(y = 10 \cdot (1.05)^{1} = 10 \cdot 1.05 = 10.5\) (not 3.6)
The equation that fits both points \((-1, 10)\) and \((1, 3.6)\) is:
**\(y = 6 \cdot (0.6)^x\)**
1. **Equation: \(y = 6 \cdot (3.6)^x\)**
- For \(x = -1\):
\(y = 6 \cdot (3.6)^{-1} = 6 \cdot \frac{1}{3.6} = \frac{6}{3.6} = 1.67\) (not 10)
- For \(x = 1\):
\(y = 6 \cdot (3.6)^{1} = 6 \cdot 3.6 = 21.6\) (not 3.6)
2. **Equation: \(y = 6 \cdot (0.6)^x\)**
- For \(x = -1\):
\(y = 6 \cdot (0.6)^{-1} = 6 \cdot \frac{1}{0.6} = 10\) (correct)
- For \(x = 1\):
\(y = 6 \cdot (0.6)^{1} = 6 \cdot 0.6 = 3.6\) (correct)
3. **Equation: \(y = 6 \cdot 0.6x\)**
- For \(x = -1\):
\(y = 6 \cdot 0.6 \cdot -1 = -3.6\) (not 10)
- For \(x = 1\):
\(y = 6 \cdot 0.6 \cdot 1 = 3.6\) (correct)
4. **Equation: \(y = 10 \cdot (1.05)^x\)**
- For \(x = -1\):
\(y = 10 \cdot (1.05)^{-1} = 10 \cdot \frac{1}{1.05} \approx 9.52\) (not 10)
- For \(x = 1\):
\(y = 10 \cdot (1.05)^{1} = 10 \cdot 1.05 = 10.5\) (not 3.6)
The equation that fits both points \((-1, 10)\) and \((1, 3.6)\) is:
**\(y = 6 \cdot (0.6)^x\)**