To find the exponential equation that corresponds to the points given in the graph, we can use the general form of an exponential function:
\[ y = ab^x \]
where:
- \( a \) is the y-intercept (the value of \( y \) when \( x = 0 \)),
- \( b \) is the growth factor.
From the points provided:
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When \( x = 0 \), \( y = 1 \). This gives us the value of \( a \): \[ y = ab^0 \implies 1 = a \cdot 1 \implies a = 1 \]
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We also know the point \( (1, 3) \). We can use this point to find \( b \): \[ y = 1 \cdot b^1 \implies 3 = b \implies b = 3 \]
Now we have both \( a \) and \( b \):
- \( a = 1 \)
- \( b = 3 \)
Thus, the exponential equation is:
\[ y = 1 \cdot 3^x \]
or simply:
\[ y = 3^x \]
This equation represents the exponential curve described by the graph.