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.
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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 \( a = 8 \).
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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.