Question

Use the graoh to answer the question.

The graph shows an exponentially rising line passing through (1, 3) and (0, 1)

Write the exponential equation shown in the graph.

Answer 1

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:
1. When \( x = 0 \), \( y = 1 \). This gives us the value of \( a \):
\[
y = ab^0 \implies 1 = a \cdot 1 \implies a = 1
\]

2. 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.