To answer this question and plot a graph of count rate against time, follow these steps:
1. Analyze the data provided:
- Time (s): [0, 5, 10, 15, 20]
- Count rate (per minute): [590, 318, 172, 84, 50]
2. Prepare the graph:
- The x-axis will represent time in seconds.
- The y-axis will represent the count rate per minute.
3. Plot the points on the graph:
- (0, 590)
- (5, 318)
- (10, 172)
- (15, 84)
- (20, 50)
4. Connect the points with a line to represent the change in count rate over time.
5. Label the axes and add a title to the graph.
Let's go through detailed steps to manually create the graph:
### Step-by-Step Process:
1. Draw the Axes:
- Draw a vertical axis (y-axis) for the count rate.
- Draw a horizontal axis (x-axis) for time.
2. Label the Axes:
- Label the y-axis as "Count Rate (per minute)".
- Label the x-axis as "Time (s)".
3. Choose a Suitable Scale:
- For the x-axis: Divide the range 0 to 20 seconds into appropriate equal intervals, considering the data points at 0, 5, 10, 15, and 20 seconds.
- For the y-axis: Since the count rate ranges from 50 to 590, choose a scale that covers this range. For instance, you could use intervals of 50 or 100.
4. Plot the Data Points:
- Locate and plot the points (0, 590), (5, 318), (10, 172), (15, 84), (20, 50) on the graph using the scales you chose.
5. Draw the Graph:
- Connect the data points with straight lines. This may help in visualizing how the count rate decreases over time.
6. Title the Graph:
- Add a title to the graph, such as "Count Rate vs. Time".
### Below is the representation of the steps:
#### Table for reference:
[tex]\[
\begin{array}{c|c}
\text{Time (s)} & \text{Count Rate (per minute)} \\
\hline
0 & 590 \\
5 & 318 \\
10 & 172 \\
15 & 84 \\
20 & 50 \\
\end{array}
\][/tex]
#### Graph Representation (Using textual representation):
```
Count Rate (per minute)
|
|
|
| | (0, 590)
| | |
| 600 |------------------------------------------------------
| |
| |
| 500 |
| | | (5, 318)
| |---------------------------------------
| |
| |
| 400 |
| |
| |
| 300 |
| |
| | (10, 172)
| |-------------------
| |
| 200 |
|
| | (15, 84)
| |---------------------
| 100 |
| |
| |
| 0
| | (20, 50)
|--------------------------------------------------------------
Time (s)
0 5 10 15 20
```
Ensure to get accurate placements while plotting on graph paper for precise readings.
### Final Notes:
- Make use of graph paper for plotting the data points for better accuracy.
- Ensure the scales on both axes are marked correctly and consistently.
- Clearly label the axes and give your graph a descriptive title to make the data representation clear and meaningful.
