To complete the chart for the given equation \( f(x) = 350(1.22)^x \), we need to calculate the population of beetles for each month from \( x = 0 \) to \( x = 5 \):
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For \( x = 0 \): \[ f(0) = 350(1.22)^0 = 350 \times 1 = 350 \]
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For \( x = 1 \): \[ f(1) = 350(1.22)^1 = 350 \times 1.22 = 427 \]
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For \( x = 2 \): \[ f(2) = 350(1.22)^2 = 350 \times 1.4884 \approx 520 \]
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For \( x = 3 \): \[ f(3) = 350(1.22)^3 = 350 \times 1.8147 \approx 635 \]
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For \( x = 4 \): \[ f(4) = 350(1.22)^4 = 350 \times 2.2135 \approx 775 \]
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For \( x = 5 \): \[ f(5) = 350(1.22)^5 = 350 \times 2.7080 \approx 948 \]
The completed chart would look like this:
| Month (x) | Population (f(x)) | |-----------|--------------------| | 0 | 350 | | 1 | 427 | | 2 | ~520 | | 3 | ~635 | | 4 | ~775 | | 5 | ~948 |
Now you can plot the points:
- (0, 350)
- (1, 427)
- (2, 520)
- (3, 635)
- (4, 775)
- (5, 948)
These points will show an increasing curve.
Given your choices, this corresponds to:
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 is the correct choice as the beetle population is growing with time.
1 answer