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Calculate the percentages of a population of German cockroaches with and without glucose aversion at two points in time.

The passage describes glucose aversion in German cockroaches. The German cockroach is considered a pest in many parts of the world. One method to control cockroach populations is to use poisoned food containing sugars such as glucose. Many cockroaches are attracted to these sugars, and once consumed, the poison kills them.

Some German cockroaches have a trait called glucose aversion, meaning they do not eat foods containing glucose and thus avoid poisoning.

The table below describes a possible population of German cockroaches at the start of a period of time and at the end of that period. It shows the number of cockroaches with and without the glucose aversion trait at each point in time.

| Time | Number with Glucose Aversion | Number without Glucose Aversion |
|-------|------------------------------|---------------------------------|
| Start | 272 | 578 |
| End | 399 | 301 |

Complete the table by calculating the percentage of cockroaches with and without glucose aversion at the start and end points.

Answer :

To solve this problem, we need to calculate the percentage of German cockroaches with and without the glucose aversion trait at the start and end of the given period.

We'll calculate the percentages for both conditions using the formula:

[tex]\text{Percentage} = \left( \frac{\text{Number in specific condition}}{\text{Total population}} \right) \times 100[/tex]

1. Start of the Period:

  • Total population at the start = 272 (with glucose aversion) + 578 (without glucose aversion) = 850

  • Percentage with glucose aversion:
    [tex]\left( \frac{272}{850} \right) \times 100 \approx 32.0\%[/tex]

  • Percentage without glucose aversion:
    [tex]\left( \frac{578}{850} \right) \times 100 \approx 68.0\%[/tex]

2. End of the Period:

  • Total population at the end = 399 (with glucose aversion) + 301 (without glucose aversion) = 700

  • Percentage with glucose aversion:
    [tex]\left( \frac{399}{700} \right) \times 100 \approx 57.0\%[/tex]

  • Percentage without glucose aversion:
    [tex]\left( \frac{301}{700} \right) \times 100 \approx 43.0\%[/tex]

These calculations show how the percentage of German cockroaches with and without the glucose aversion trait in the population changed over the period. The increase in the percentage of cockroaches with glucose aversion suggests that this trait might be providing a survival advantage in environments where food contains glucose.

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