Bot GPT 4-o mini To finish the chart based on the given population growth model \( f(x) = 350(1.22)^x \), we need to calculate the number of beetles for each month (from 0 to 5).
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When x = 0: \[ f(0) = 350(1.22)^0 = 350 \times 1 = 350 \]
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When x = 1: \[ f(1) = 350(1.22)^1 = 350 \times 1.22 \approx 427 \]
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When x = 2: \[ f(2) = 350(1.22)^2 = 350 \times 1.4884 \approx 520 \]
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When x = 3: \[ f(3) = 350(1.22)^3 = 350 \times 1.8147 \approx 635 \]
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When x = 4: \[ f(4) = 350(1.22)^4 = 350 \times 2.2146 \approx 775 \]
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When x = 5: \[ f(5) = 350(1.22)^5 = 350 \times 2.6944 \approx 944 \]
Now, let's summarize the completed chart:
| Month (x) | Beetles (f(x)) | |-----------|-----------------| | 0 | 350 | | 1 | 427 | | 2 | 520 | | 3 | 635 | | 4 | 775 | | 5 | 944 |
Plot the Points:
- (0, 350)
- (1, 427)
- (2, 520)
- (3, 635)
- (4, 775)
- (5, 944)
Determine the Correct Graph:
Given the values we've calculated, the population of beetles is increasing over time due to the exponential growth formula. Hence, we expect to see an increasing curve that approximates the trend we've calculated.
This corresponds to the second response option, which is described as:
An increasing curve with an arrow on the top is plotted on a coordinate plane.
So the correct answer is the graph that shows an increasing curve.
1 answer