To write the exponential equation of the form \( y = a \cdot b^x \), we need to determine the values of \( a \) and \( b \).
From the graph, we know that:
- The point \( (0, 10) \) indicates that when \( x = 0 \), \( y = 10 \). This tells us that \( a = 10 \) because \( y = a \cdot b^0 = a \).
So, we have: \[ y = 10 \cdot b^x \]
Next, we use the point \( (1, 10.5) \) to find \( b \): \[ 10.5 = 10 \cdot b^1 \] Dividing both sides by 10 gives: \[ b = \frac{10.5}{10} = 1.05 \]
Now, we can substitute \( a \) and \( b \) into the equation: \[ y = 10 \cdot 1.05^x \]
Therefore, the exponential equation shown in the graph is: \[ y = 10 \cdot 1.05^x \]
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