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

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

Answer 2

To express the exponential equation shown in the graph, we often follow the general form of an exponential function, which is:

\[ y = ab^{x} \]

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

Without the specific details or numerical values from the graph, I cannot provide the exact equation. However, if you notice the y-intercept and the growth behavior of the graph, you can determine the values of \( a \) and \( b \).

Please check the y-intercept (the value when \( x = 0 \)) to find \( a \), and observe how quickly the values of \( y \) increase (or decrease) as \( x \) changes to determine \( b \).

If you have those values or you can describe the growth pattern, please share them, and I can help you formulate the exact equation.

Answer 3

Given the points \((0, 1)\) and \((1, 3)\):

1. **Determine the initial value \(a\)**:
The point \((0, 1)\) indicates that the value of the function when \(x = 0\) (the y-intercept) is \(1\). Thus, \(a = 1\).

2. **Determine the base \(b\)**:
To find \(b\), we can use the point \((1, 3)\):
\[
y = ab^x
\]
Substituting \(x = 1\) and \(y = 3\):
\[
3 = 1 \cdot b^1
\]
This simplifies to:
\[
b = 3
\]

3. **Write the exponential equation**:
Combining \(a\) and \(b\), the equation is:
\[
y = 1 \cdot 3^x
\]
which simplifies to:
\[
y = 3^x
\]

Therefore, the exponential equation of the graph is:
\[
y = 3^x
\]