Use the table to answer the question.
0 350
1
2
3
4
5 A certain population of beetles is increasing at a rate of 22% per month. If there are currently 350 beetles, the equation f(x)=350(1.22)x can be used to model the situation. Finish the chart and plot the points to determine which graph correctly displays the situation.(1 point)
Responses
An increasing curve with an arrow on the top is plotted on a coordinate plane. The x-axis for months ranges from 0 to 2,000 in increments of 200. The y-axis for Beetles ranges from 0 to 10 in increments of 1.
Image with alt text: An increasing curve with an arrow on the top is plotted on a coordinate plane. The x-axis for months ranges from 0 to 2,000 in increments of 200. The y-axis for Beetles ranges from 0 to 10 in increments of 1.
A decreasing curve with an arrow at the end 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 350 in increments of 50.
Image with alt text: A decreasing curve with an arrow at the end 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 350 in increments of 50.
A decreasing curve with an arrow at the end 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 350 in increments of 50.
Image with alt text: A decreasing curve with an arrow at the end 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 350 in increments of 50.
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.
Image with alt text: 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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To determine which graph correctly displays the situation, we can use the equation f(x)=350(1.22)x and the table given.
Using the equation, we can calculate the values for each month:
For month 1: f(1) = 350(1.22)1 = 427 (approximately)
For month 2: f(2) = 350(1.22)2 = 521 (approximately)
For month 3: f(3) = 350(1.22)3 = 635.02 (approximately)
For month 4: f(4) = 350(1.22)4 = 772.53 (approximately)
For month 5: f(5) = 350(1.22)5 = 937.68 (approximately)
Now let's compare these values with the options given.
Option 1: The x-axis ranges from 0 to 2,000, which is not necessary for the given situation. The y-axis ranges from 0 to 10, which is not sufficient to represent the increasing population of beetles.
Option 2: The x-axis ranges from 0 to 10, which is appropriate for the given situation. The y-axis ranges from 0 to 350, which is sufficient to represent the increasing population of beetles.
Option 3: The x-axis ranges from 0 to 10, which is appropriate for the given situation. The y-axis ranges from 0 to 350, which is sufficient to represent the increasing population of beetles.
Option 4: The x-axis ranges from 0 to 10, which is appropriate for the given situation. The y-axis ranges from 0 to 2,000, which is not necessary for the given situation.
Based on the calculations and comparisons, it can be concluded that option 3 correctly displays the situation.