Question
Use the graph to answer the question.
image shows x axis from -5 to 5 and y from 10 down to 0. points 0, 8 and 1, 6 are shown
Which equation is shown in the graph? (1 point) Responses y=8⋅(1.75)x y is equal to 8 times 1 point 7 5 to the x th power y=−8⋅(0.75)x y is equal to negative 8 times 0 point 7 5 to the x th power y=8⋅(0.75)x y is equal to 8 times 0 point 7 5 to the x th power y=(14)x
image shows x axis from -5 to 5 and y from 10 down to 0. points 0, 8 and 1, 6 are shown
Which equation is shown in the graph? (1 point) Responses y=8⋅(1.75)x y is equal to 8 times 1 point 7 5 to the x th power y=−8⋅(0.75)x y is equal to negative 8 times 0 point 7 5 to the x th power y=8⋅(0.75)x y is equal to 8 times 0 point 7 5 to the x th power y=(14)x
Answers
GPT-4o mini
To determine which equation is shown in the graph based on the provided points (0, 8) and (1, 6), we can analyze the potential equations.
1. **Point (0, 8)**: This indicates that when \( x = 0 \), \( y \) is 8. In an exponential function of the form \( y = a \cdot b^x \), when \( x = 0 \), \( y = a \). This means \( a = 8 \).
2. **Point (1, 6)**: This point indicates that when \( x = 1 \), \( y \) is 6. We can use this to help find \( b \). Substituting into the equation gives:
\[ 6 = 8 \cdot b^1 \]
\[ b = \frac{6}{8} = 0.75 \]
Now, substituting \( a \) and \( b \) back into the equation gives:
\[ y = 8 \cdot (0.75)^x \]
Looking at the potential responses given:
- \( y = 8 \cdot (1.75)^x \)
- \( y = -8 \cdot (0.75)^x \)
- \( y = 8 \cdot (0.75)^x \)
- \( y = (14)^x \)
The correct equation that matches our findings based on points (0, 8) and (1, 6) is:
\[ y = 8 \cdot (0.75)^x \]
So the correct response is:
**y = 8⋅(0.75)^x**.
1. **Point (0, 8)**: This indicates that when \( x = 0 \), \( y \) is 8. In an exponential function of the form \( y = a \cdot b^x \), when \( x = 0 \), \( y = a \). This means \( a = 8 \).
2. **Point (1, 6)**: This point indicates that when \( x = 1 \), \( y \) is 6. We can use this to help find \( b \). Substituting into the equation gives:
\[ 6 = 8 \cdot b^1 \]
\[ b = \frac{6}{8} = 0.75 \]
Now, substituting \( a \) and \( b \) back into the equation gives:
\[ y = 8 \cdot (0.75)^x \]
Looking at the potential responses given:
- \( y = 8 \cdot (1.75)^x \)
- \( y = -8 \cdot (0.75)^x \)
- \( y = 8 \cdot (0.75)^x \)
- \( y = (14)^x \)
The correct equation that matches our findings based on points (0, 8) and (1, 6) is:
\[ y = 8 \cdot (0.75)^x \]
So the correct response is:
**y = 8⋅(0.75)^x**.