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Graph this function.

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

1 answer

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!