Question
Use the table to answer the question.
0 350
1
2
3
4
5 A certain population of beetles is increasing at a rate of 22% per month. If there are currently 350 beetles, the equation f(x)=350(1.22)^x can be used to model the situation. Finish the chart and plot the points to determine which graph correctly displays the situation.(1 point)
Responses
A decreasing curve with an arrow at the end is plotted on a coordinate plane. The x-axis for months ranges from 0 to 10 in increments of 1. The y-axis for Beetles ranges from 0 to 350 in increments of 50.
Image with alt text: A decreasing curve with an arrow at the end is plotted on a coordinate plane. The x-axis for months ranges from 0 to 10 in increments of 1. The y-axis for Beetles ranges from 0 to 350 in increments of 50.
An increasing curve with an arrow on the top is plotted on a coordinate plane. The x-axis for months ranges from 0 to 10 in increments of 1. The y-axis for Beetles ranges from 0 to 2000 in increments of 250.
Image with alt text: An increasing curve with an arrow on the top is plotted on a coordinate plane. The x-axis for months ranges from 0 to 10 in increments of 1. The y-axis for Beetles ranges from 0 to 2000 in increments of 250.
An increasing curve with an arrow on the top is plotted on a coordinate plane. The x-axis for months ranges from 0 to 2,000 in increments of 200. The y-axis for Beetles ranges from 0 to 10 in increments of 1.
Image with alt text: An increasing curve with an arrow on the top is plotted on a coordinate plane. The x-axis for months ranges from 0 to 2,000 in increments of 200. The y-axis for Beetles ranges from 0 to 10 in increments of 1.
A decreasing curve with an arrow at the end is plotted on a coordinate plane. The x-axis for months ranges from 0 to 10 in increments of 1. The y-axis for Beetles ranges from 0 to 350 in increments of 50.
Image with alt text: A decreasing curve with an arrow at the end is plotted on a coordinate plane. The x-axis for months ranges from 0 to 10 in increments of 1. The y-axis for Beetles ranges from 0 to 350 in increments of 50.
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0 350
1
2
3
4
5 A certain population of beetles is increasing at a rate of 22% per month. If there are currently 350 beetles, the equation f(x)=350(1.22)^x can be used to model the situation. Finish the chart and plot the points to determine which graph correctly displays the situation.(1 point)
Responses
A decreasing curve with an arrow at the end is plotted on a coordinate plane. The x-axis for months ranges from 0 to 10 in increments of 1. The y-axis for Beetles ranges from 0 to 350 in increments of 50.
Image with alt text: A decreasing curve with an arrow at the end is plotted on a coordinate plane. The x-axis for months ranges from 0 to 10 in increments of 1. The y-axis for Beetles ranges from 0 to 350 in increments of 50.
An increasing curve with an arrow on the top is plotted on a coordinate plane. The x-axis for months ranges from 0 to 10 in increments of 1. The y-axis for Beetles ranges from 0 to 2000 in increments of 250.
Image with alt text: An increasing curve with an arrow on the top is plotted on a coordinate plane. The x-axis for months ranges from 0 to 10 in increments of 1. The y-axis for Beetles ranges from 0 to 2000 in increments of 250.
An increasing curve with an arrow on the top is plotted on a coordinate plane. The x-axis for months ranges from 0 to 2,000 in increments of 200. The y-axis for Beetles ranges from 0 to 10 in increments of 1.
Image with alt text: An increasing curve with an arrow on the top is plotted on a coordinate plane. The x-axis for months ranges from 0 to 2,000 in increments of 200. The y-axis for Beetles ranges from 0 to 10 in increments of 1.
A decreasing curve with an arrow at the end is plotted on a coordinate plane. The x-axis for months ranges from 0 to 10 in increments of 1. The y-axis for Beetles ranges from 0 to 350 in increments of 50.
Image with alt text: A decreasing curve with an arrow at the end is plotted on a coordinate plane. The x-axis for months ranges from 0 to 10 in increments of 1. The y-axis for Beetles ranges from 0 to 350 in increments of 50.
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Answers
Answer
wich one is it
Answered by
GPT-4o mini
To complete the given problem, we need to calculate the number of beetles for different months using the function \( f(x) = 350(1.22)^x \). We'll compute this for \( x = 1, 2, 3, 4, \) and \( 5 \).
### Calculations:
1. **For \( x = 0 \)**:
\( f(0) = 350(1.22)^0 = 350 \) (Already given)
2. **For \( x = 1 \)**:
\( f(1) = 350(1.22)^1 = 350 \times 1.22 = 427 \)
3. **For \( x = 2 \)**:
\( f(2) = 350(1.22)^2 = 350 \times 1.4884 \approx 521 \)
4. **For \( x = 3 \)**:
\( f(3) = 350(1.22)^3 = 350 \times 1.8140 \approx 634 \)
5. **For \( x = 4 \)**:
\( f(4) = 350(1.22)^4 = 350 \times 2.2117 \approx 774 \)
6. **For \( x = 5 \)**:
\( f(5) = 350(1.22)^5 = 350 \times 2.698 \approx 944 \)
### Completed Chart:
| Months (x) | Beetles (f(x)) |
|------------|-----------------|
| 0 | 350 |
| 1 | 427 |
| 2 | 521 |
| 3 | 634 |
| 4 | 774 |
| 5 | 944 |
### Graphing:
When plotting these points on a coordinate plane, we can see that they form an increasing curve as the number of beetles increases exponentially with each passing month.
### Conclusion:
Looking at the given responses, the correct one is:
- **An increasing curve with an arrow on the top is plotted on a coordinate plane. The x-axis for months ranges from 0 to 10 in increments of 1. The y-axis for Beetles ranges from 0 to 2000 in increments of 250.**
This choice represents the exponential growth of the population, which is consistent with the calculations made.
### Calculations:
1. **For \( x = 0 \)**:
\( f(0) = 350(1.22)^0 = 350 \) (Already given)
2. **For \( x = 1 \)**:
\( f(1) = 350(1.22)^1 = 350 \times 1.22 = 427 \)
3. **For \( x = 2 \)**:
\( f(2) = 350(1.22)^2 = 350 \times 1.4884 \approx 521 \)
4. **For \( x = 3 \)**:
\( f(3) = 350(1.22)^3 = 350 \times 1.8140 \approx 634 \)
5. **For \( x = 4 \)**:
\( f(4) = 350(1.22)^4 = 350 \times 2.2117 \approx 774 \)
6. **For \( x = 5 \)**:
\( f(5) = 350(1.22)^5 = 350 \times 2.698 \approx 944 \)
### Completed Chart:
| Months (x) | Beetles (f(x)) |
|------------|-----------------|
| 0 | 350 |
| 1 | 427 |
| 2 | 521 |
| 3 | 634 |
| 4 | 774 |
| 5 | 944 |
### Graphing:
When plotting these points on a coordinate plane, we can see that they form an increasing curve as the number of beetles increases exponentially with each passing month.
### Conclusion:
Looking at the given responses, the correct one is:
- **An increasing curve with an arrow on the top is plotted on a coordinate plane. The x-axis for months ranges from 0 to 10 in increments of 1. The y-axis for Beetles ranges from 0 to 2000 in increments of 250.**
This choice represents the exponential growth of the population, which is consistent with the calculations made.
Answered by
GPT-4o mini
The correct response is:
**An increasing curve with an arrow on the top is plotted on a coordinate plane. The x-axis for months ranges from 0 to 10 in increments of 1. The y-axis for Beetles ranges from 0 to 2000 in increments of 250.**
This choice appropriately reflects the exponential increase in the beetle population over time, corresponding to the increasing values calculated from the function \( f(x) = 350(1.22)^x \).
**An increasing curve with an arrow on the top is plotted on a coordinate plane. The x-axis for months ranges from 0 to 10 in increments of 1. The y-axis for Beetles ranges from 0 to 2000 in increments of 250.**
This choice appropriately reflects the exponential increase in the beetle population over time, corresponding to the increasing values calculated from the function \( f(x) = 350(1.22)^x \).
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