Question

A certain population of beetles are 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.
Complete the table using the equation and a calculator. Round to the nearest tenth.(3 points)
0 350
1
2
3
4
5

Answer 1

To complete the table using the equation \( f(x) = 350(1.22)^x \), we'll calculate the values for \( f(x) \) for \( x = 0, 1, 2, 3, 4, 5 \).

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

2. For \( x = 1 \):
\[
f(1) = 350(1.22)^1 = 350(1.22) \approx 427.0
\]

3. For \( x = 2 \):
\[
f(2) = 350(1.22)^2 = 350(1.4884) \approx 520.9
\]

4. For \( x = 3 \):
\[
f(3) = 350(1.22)^3 = 350(1.8049) \approx 631.7
\]

5. For \( x = 4 \):
\[
f(4) = 350(1.22)^4 = 350(2.1997) \approx 769.9
\]

6. For \( x = 5 \):
\[
f(5) = 350(1.22)^5 = 350(2.6756) \approx 936.5
\]

Now we can summarize the values in a table:

| \( x \) | \( f(x) \) |
|:---------:|:-------------:|
| 0 | 350.0 |
| 1 | 427.0 |
| 2 | 520.9 |
| 3 | 631.7 |
| 4 | 769.9 |
| 5 | 936.5 |

Please let me know if you need any further assistance!