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
1 427.0
2 520.9
3 631.7
4 769.9
5 936.5
Question 2
Which graph correctly displays the table above?(1 point)
Responses

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1 answer

To complete the table and confirm the values, we will use the equation \( f(x) = 350(1.22)^x \) for different values of \( x \):

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

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

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

  4. When \( x = 3 \): \[ f(3) = 350(1.22)^3 = 350 \times 1.8145 \approx 631.7 \]

  5. When \( x = 4 \): \[ f(4) = 350(1.22)^4 = 350 \times 2.2074 \approx 769.9 \]

  6. When \( x = 5 \): \[ f(5) = 350(1.22)^5 = 350 \times 2.6894 \approx 941.3 \] (Note: Previously you had 936.5, but this is the correct calculation from the equation using rounding appropriately.)

Now, the complete table is as follows:

| \( x \) | \( f(x) \) | |:---------:|:------------:| | 0 | 350.0 | | 1 | 427.0 | | 2 | 520.9 | | 3 | 631.7 | | 4 | 769.9 | | 5 | 941.3 |

Question 2

To determine which graph displays the table, you would need to look for a graph showing an exponential growth pattern, where the y-values increase rapidly as \( x \) increases, starting from 350 and going upwards.

  1. The graph should start at 350 when \( x = 0 \).
  2. As \( x \) increases, the graph should slope sharply upwards reflecting the 22% growth rate.

You can identify the correct graph by looking for these characteristics. Since I cannot view the graphs you've provided, I recommend selecting the graph that best embodies these features.