To fill out the population chart of beetles using the equation \( f(x) = 350(1.22)^x \), we will calculate the number of beetles for each month \( x \) from 0 to 5.
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For \( x = 0 \): \[ f(0) = 350(1.22)^0 = 350(1) = 350 \]
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For \( x = 1 \): \[ f(1) = 350(1.22)^1 = 350(1.22) \approx 427 \]
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For \( x = 2 \): \[ f(2) = 350(1.22)^2 = 350(1.4884) \approx 521 \]
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For \( x = 3 \): \[ f(3) = 350(1.22)^3 = 350(1.8144) \approx 635 \]
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For \( x = 4 \): \[ f(4) = 350(1.22)^4 = 350(2.2198) \approx 777 \]
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For \( x = 5 \): \[ f(5) = 350(1.22)^5 = 350(2.7081) \approx 947 \]
Now, let's summarize the complete data in a chart format:
| Month (x) | Beetles (f(x)) | |-----------|-----------------| | 0 | 350 | | 1 | 427 | | 2 | 521 | | 3 | 635 | | 4 | 777 | | 5 | 947 |
Plot Points
The points to plot are:
- (0, 350)
- (1, 427)
- (2, 521)
- (3, 635)
- (4, 777)
- (5, 947)
Graph Selection
The growth rate of 22% per month means that the graph of the function will be an increasing curve, not a decreasing one. Therefore, the correct graph to choose must show an increasing trend that best matches the calculated points.
Given the descriptions of the images you provided:
- A decreasing curve with an arrow at the end.
- An increasing curve with an arrow on the top.
- A decreasing curve with an arrow at the end.
The correct response would be the second graph (the increasing curve), as it reflects the nature of exponential growth in the population of beetles.
1 answer