To find the exponential equation based on the given points (1, 3) and (0, 1), we can start with the general form of an exponential function:
\[ y = ab^x \]
Where:
- \( a \) is the initial value (the y-intercept, which we find at \( x = 0 \)),
- \( b \) is the base of the exponential function.
From the point (0, 1), we can see that when \( x = 0 \), \( y = 1 \). According to the equation, this gives us:
\[ y = ab^0 \] \[ 1 = a \cdot 1 \] So, we find \( a = 1 \).
Now we have:
\[ y = 1 \cdot b^x \] \[ y = b^x \]
Next, we can use the other point (1, 3) to find \( b \):
When \( x = 1 \), \( y = 3 \):
\[ 3 = b^1 \] \[ b = 3 \]
Now, we can write the full equation:
\[ y = 3^x \]
So, the exponential equation shown in the graph is:
\[ y = 3^x \]
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