Question

Use the graph to answer the question.

Write the exponential equation shown in the graph.

A coordinate plane going from negative 5 to 5 in increments of 1 labeled every 5 units on the x-axis and from negative 1 to 10 in increments of 1 labeled every 5 units on the y-axis.

(1 point)
The equation is $$
.

Answer 1

points on the graph are (1,3) and (0,1)

Answer 2

To write the exponential equation shown in the graph, we typically look for the general form of an exponential function, which is:

\[ y = ab^x \]

where:
- \( a \) is the initial value (the y-intercept when \( x = 0 \))
- \( b \) is the base of the exponential function, which determines the growth (if \( b > 1 \)) or decay (if \( 0 < b < 1 \)).

To determine the specific values of \( a \) and \( b \), we would need key points from the graph. For example, if the graph shows that when \( x = 0 \), \( y = 2 \), then \( a = 2 \).

Next, you would look for another point on the graph, say \( (1, 4) \):
- Using these points, we can set up the equations:

1. At \( x = 0 \):
\[ y = ab^0 = a \rightarrow a = 2 \]

2. At \( x = 1 \):
\[ y = ab^1 \rightarrow 4 = 2b \rightarrow b = 2 \]

So the exponential equation would be:

\[ y = 2(2^x) \]

Please provide the key points or characteristics from the graph so I can help you find the exact equation.

Answer 3

Given the points on the graph (0, 1) and (1, 3), we can find the exponential equation in the form:

\[
y = ab^x
\]

**Step 1:** Find \(a\) using the point (0, 1).

When \(x = 0\):
\[
y = ab^0 = a = 1
\]

So, \(a = 1\).

**Step 2:** Use the second point (1, 3) to find \(b\).

When \(x = 1\):
\[
y = ab^1 = 1 \cdot b = b
\]
From the point (1, 3):
\[
b = 3
\]

**Step 3:** Substitute \(a\) and \(b\) into the exponential equation.

Now we have:
\[
y = 1 \cdot 3^x
\]

Thus, the exponential equation shown in the graph is:

\[
y = 3^x
\]

So, the final answer is:
\[
\boxed{y = 3^x}
\]