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Graph this function.

y=28(4/7)^x
Plot two points to graph the function.

1 answer

To graph the function \( y = 28 \left( \frac{4}{7} \right)^x \), we can plot two points by choosing different values for \( x \).

Step 1: Calculate Points

  1. When \( x = 0 \): \[ y = 28 \left( \frac{4}{7} \right)^0 = 28(1) = 28 \] So we have the point \( (0, 28) \).

  2. When \( x = 1 \): \[ y = 28 \left( \frac{4}{7} \right)^1 = 28 \left( \frac{4}{7} \right) = \frac{112}{7} = 16 \] So we have the point \( (1, 16) \).

Step 2: Summary of Points

We can summarize our points as follows:

  • Point 1: \( (0, 28) \)
  • Point 2: \( (1, 16) \)

Step 3: Behavior of the Function

The function is an exponential decay function because the base \( \frac{4}{7} \) is less than 1. As \( x \) increases, \( y \) will decrease.

Step 4: Graphing

While I cannot draw the graph for you, you can graph the points \( (0, 28) \) and \( (1, 16) \) on a coordinate system.

  1. Plot the point \( (0, 28) \).
  2. Plot the point \( (1, 16) \).
  3. Since the function is exponential decay, you would draw a smooth curve that starts at \( y = 28 \) when \( x = 0 \) and gradually decreases as \( x \) increases.

This gives you the initial shape of the graph \( y = 28 \left( \frac{4}{7} \right)^x \).