To complete the table based on the given exponential growth model \( f(x) = 350(1.22)^x \) for a population of beetles increasing at a rate of 22% per month, we'll calculate the number of beetles at each specified month:
- Month 0: \[ f(0) = 350(1.22)^0 = 350 \times 1 = 350 \]
- Month 1: \[ f(1) = 350(1.22)^1 = 350 \times 1.22 \approx 427 \]
- Month 2: \[ f(2) = 350(1.22)^2 = 350 \times 1.4884 \approx 520 \]
- Month 3: \[ f(3) = 350(1.22)^3 = 350 \times 1.8038 \approx 631 \]
- Month 4: \[ f(4) = 350(1.22)^4 = 350 \times 2.198 \approx 769 \]
- Month 5: \[ f(5) = 350(1.22)^5 = 350 \times 2.683 \approx 939 \]
Now, let's summarize the completed table:
| Month (x) | Population (f(x)) | |-----------|--------------------| | 0 | 350 | | 1 | 427 | | 2 | 520 | | 3 | 631 | | 4 | 769 | | 5 | 939 |
Conclusion
The function models exponential growth, so the graph will be an increasing curve as the population of beetles increases over time.
Therefore, the correct graph should show an increasing curve with an arrow on the top. The response that fits this description 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 graph accurately represents the growth of the beetle population over time based on the provided model.
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