Question

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

Answer 1

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.