Question

Use the graph to answer the question.

Write the exponential equation shown in the graph (1, 3) and (0, 1).



(1 point)
The equation is $$y=.

Answer 1

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:

\[ y = 3^x \]