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Graph this function.

y=5(2)^x
Plot two points to graph the function.

1 answer

To graph the function \( y = 5(2)^x \), we can plot a few points by choosing values for \( x \) and calculating the corresponding \( y \) values.

Choose Values for \( x \):

  1. Let \( x = 0 \): \[ y = 5(2)^0 = 5 \times 1 = 5 \] So, the point is \( (0, 5) \).

  2. Let \( x = 1 \): \[ y = 5(2)^1 = 5 \times 2 = 10 \] So, the point is \( (1, 10) \).

Points to Plot:

  • \( (0, 5) \)
  • \( (1, 10) \)

Plotting the Points:

  1. Point \( (0, 5) \): This is where the graph intersects the y-axis.
  2. Point \( (1, 10) \): This shows that when \( x = 1 \), \( y = 10 \).

General Shape of the Graph:

The graph of the function \( y = 5(2)^x \) is an exponential growth curve. It starts at \( y = 5 \) when \( x = 0 \) and increases rapidly as \( x \) increases.

Additional Points (Optional):

To get a better shape of the graph, you could also calculate \( y \) for \( x = -1 \):

  • For \( x = -1 \): \[ y = 5(2)^{-1} = 5 \times \frac{1}{2} = 2.5 \] This gives the point \( (-1, 2.5) \).

Summary of Points:

  • \( (-1, 2.5) \)
  • \( (0, 5) \)
  • \( (1, 10) \)

You can plot these points on Cartesian coordinates and draw a smooth curve through them, representing the exponential function. The curve will continue to rise steeply as \( x \) increases.