To determine the correct graph for the population of beetles increasing at a rate of 22% per month, we can calculate the values and plot them based on the given equation \( f(x) = 350(1.22)^x \).
Let's calculate the values for \( x = 0, 1, 2, 3, 4, 5 \):
- \( f(0) = 350(1.22)^0 = 350 \)
- \( f(1) = 350(1.22)^1 = 350 \times 1.22 \approx 427 \)
- \( f(2) = 350(1.22)^2 = 350 \times 1.4884 \approx 521 \)
- \( f(3) = 350(1.22)^3 = 350 \times 1.8155 \approx 636 \)
- \( f(4) = 350(1.22)^4 = 350 \times 2.2137 \approx 774 \)
- \( f(5) = 350(1.22)^5 = 350 \times 2.7010 \approx 945 \)
Now, let's summarize the data:
| Months (x) | Beetles (f(x)) | |------------|-----------------| | 0 | 350 | | 1 | ~427 | | 2 | ~521 | | 3 | ~636 | | 4 | ~774 | | 5 | ~945 |
Since the population is increasing over time, we expect a graph that rises as x increases.
Looking at the options provided:
- Options that describe a decreasing curve can be eliminated because the population is increasing.
- The remaining options describe increasing curves.
Based on the calculations, the population rises above 350 within the first month, so the second option seems consistent with an increasing curve that can extend to higher values reflecting the increase.
Thus, the correct choice 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.
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