Question

Question
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

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.

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.
Skip to navigation

Answer 1

To finish the chart using the equation \( f(x) = 350(1.22)^x \) for months \( x = 0, 1, 2, 3, 4, 5 \), we can compute the number of beetles at each point:

1. **For \( x = 0 \)**:
\[
f(0) = 350(1.22)^0 = 350 \quad \text{(this is already given)}
\]

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 \( x = 4 \)**:
\[
f(4) = 350(1.22)^4 = 350 \times 2.1996 \approx 770
\]

6. **For \( x = 5 \)**:
\[
f(5) = 350(1.22)^5 = 350 \times 2.6820 \approx 939
\]

Now we can summarize the obtained values in the chart:

\[
\begin{array}{|c|c|}
\hline
\text{Months (x)} & \text{Beetles (f(x))} \\
\hline
0 & 350 \\
1 & 427 \\
2 & 520 \\
3 & 631 \\
4 & 770 \\
5 & 939 \\
\hline
\end{array}
\]

Now plotting these points:

- (0, 350)
- (1, 427)
- (2, 520)
- (3, 631)
- (4, 770)
- (5, 939)

Given the data generated shows growth in the population of beetles, the correct graph should display an increasing curve.

Among your options:

1. **A decreasing curve** (incorrect)
2. **An increasing curve with an arrow on the top** (correct)
3. **An increasing curve but with incorrect scales** (incorrect)
4. **A decreasing curve again** (incorrect)

Therefore, the correct graph response is **the increasing curve with an arrow on the top** that aligns with the calculated values for beetle population.