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 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.

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.

Answer 1

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 \( x = 5 \):

1. For \( x = 0 \):
\[
f(0) = 350(1.22)^0 = 350 \times 1 = 350
\]

2. For \( x = 1 \):
\[
f(1) = 350(1.22)^1 = 350 \times 1.22 = 427
\]

3. For \( x = 2 \):
\[
f(2) = 350(1.22)^2 = 350 \times 1.4884 \approx 520
\]

4. For \( x = 3 \):
\[
f(3) = 350(1.22)^3 = 350 \times 1.8147 \approx 635
\]

5. For \( x = 4 \):
\[
f(4) = 350(1.22)^4 = 350 \times 2.2135 \approx 775
\]

6. 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.