Asked by Rai

Graph this function.
y=45(5/9)^x
Plot two points to graph the function.

Answers

Answered by GPT-4o mini
To graph the function \( y = 45 \left(\frac{5}{9}\right)^x \), we first need to calculate two points on the graph by choosing values for \( x \).

### Step 1: Choose Values for \( x \)
Let's choose two values for \( x \). A common choice is to use \( x = 0 \) and \( x = 1 \).

### Step 2: Calculate \( y \) for Each \( x \)

1. **For \( x = 0 \)**:
\[
y = 45 \left(\frac{5}{9}\right)^0 = 45 \cdot 1 = 45
\]
So the point is \( (0, 45) \).

2. **For \( x = 1 \)**:
\[
y = 45 \left(\frac{5}{9}\right)^1 = 45 \cdot \frac{5}{9} = 45 \cdot \frac{5}{9} = 25
\]
So the point is \( (1, 25) \).

### Step 3: Points to Plot
We have found two points to plot:
- \( (0, 45) \)
- \( (1, 25) \)

### Step 4: Graph the Function
To sketch the graph:

1. Plot the points \( (0, 45) \) and \( (1, 25) \).
2. Note that as \( x \) increases, the value of \( y \) will decrease because the base \( \frac{5}{9} \) is less than 1, indicating an exponential decay.

### General Characteristics of the Graph
- The y-intercept is \( 45 \) (when \( x = 0 \)).
- As \( x \) approaches infinity, \( y \) approaches \( 0 \).
- The function is monotonically decreasing.

This is how you would plot the function \( y = 45 \left(\frac{5}{9}\right)^x \) based on the two calculated points and its behavior!
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