Question
Use the table to answer the question. is it a b c or d?
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
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.
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 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.
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is it a b c or d ?
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
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.
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 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.
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is it a b c or d ?
Answers
GPT-4o mini
To determine which graph correctly displays the population growth of beetles according to the model \( f(x) = 350(1.22)^x \), we need to calculate the values of \( f(x) \) for the given months (0 to 5).
1. **For \( x = 0 \)**:
\[
f(0) = 350(1.22)^0 = 350
\]
2. **For \( x = 1 \)**:
\[
f(1) = 350(1.22)^1 = 350 \times 1.22 \approx 427
\]
3. **For \( x = 2 \)**:
\[
f(2) = 350(1.22)^2 = 350 \times 1.4884 \approx 520
\]
4. **For \( x = 3 \)**:
\[
f(3) = 350(1.22)^3 = 350 \times 1.8049 \approx 631
\]
5. **For \( x = 4 \)**:
\[
f(4) = 350(1.22)^4 = 350 \times 2.2087 \approx 772
\]
6. **For \( x = 5 \)**:
\[
f(5) = 350(1.22)^5 = 350 \times 2.698 \approx 944
\]
Now, the population of beetles is increasing over time. The values of \( f(x) \) at \( x = 0, 1, 2, 3, 4, 5 \) are respectively:
- 350, 427, 520, 631, 772, 944.
This shows a clear increasing trend.
Given the options:
- **A and C** describe decreasing curves, which cannot be correct.
- **D** involves an inappropriate scale and represents a flat range for beetle population counts which is incorrect.
Thus, the correct response is **B**, as it depicts an increasing curve with an appropriate scale for the population growth of beetles.
1. **For \( x = 0 \)**:
\[
f(0) = 350(1.22)^0 = 350
\]
2. **For \( x = 1 \)**:
\[
f(1) = 350(1.22)^1 = 350 \times 1.22 \approx 427
\]
3. **For \( x = 2 \)**:
\[
f(2) = 350(1.22)^2 = 350 \times 1.4884 \approx 520
\]
4. **For \( x = 3 \)**:
\[
f(3) = 350(1.22)^3 = 350 \times 1.8049 \approx 631
\]
5. **For \( x = 4 \)**:
\[
f(4) = 350(1.22)^4 = 350 \times 2.2087 \approx 772
\]
6. **For \( x = 5 \)**:
\[
f(5) = 350(1.22)^5 = 350 \times 2.698 \approx 944
\]
Now, the population of beetles is increasing over time. The values of \( f(x) \) at \( x = 0, 1, 2, 3, 4, 5 \) are respectively:
- 350, 427, 520, 631, 772, 944.
This shows a clear increasing trend.
Given the options:
- **A and C** describe decreasing curves, which cannot be correct.
- **D** involves an inappropriate scale and represents a flat range for beetle population counts which is incorrect.
Thus, the correct response is **B**, as it depicts an increasing curve with an appropriate scale for the population growth of beetles.