A student does an experiment for a science fair to study whether temperature affects the timing of a cricket's chirps. The student keeps a cricket in an enclosed box that is heated to different temperatures each day for twelve days. The student records the cricket's chirps by using a sound-activated microphone so that the timing of the chirps can be measured. The student records the results of the experiment in the table below.
| Day | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Temperature ($^{\circ}C$) | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 |
| Average time between chirps (sec) | 2.5 | 2.6 | 2.2 | 2.3 | 2.0 | 1.8 | 1.9 | 1.8 | 1.4 | 1.2 | 1.5 | 1.1 |
Which generalization can be made from the data in the table?
A. The higher the temperature, the fewer chirps there will be in 10 seconds.
B. The chirps occur closer together as the temperature increases.
C. The chirps become farther apart as the temperature increases.
D. There is no relationship between temperature and the time between chirps.
Answer (2)
Analyze the data: Observe that as temperature increases, the average time between chirps tends to decrease.
Calculate chirps per 10 seconds: Determine the number of chirps in 10 seconds for each temperature.
Identify the trend: Note that as temperature increases, the number of chirps in 10 seconds generally increases, meaning chirps occur closer together.
Generalize the relationship: Conclude that the chirps occur closer together as the temperature increases. T h ec hi r p socc u rc l oser t o g e t h er a s t h e t e m p er a t u re in cre a ses .
Explanation
Understanding the Problem We are given a table of temperatures and the corresponding average time between cricket chirps. We need to determine the relationship between the temperature and the time between chirps.
Analyzing the Trend As the temperature increases from 21 to 32 degrees Celsius, the average time between chirps generally decreases from 2.5 seconds to 1.1 seconds. Let's calculate the number of chirps in 10 seconds for each temperature to see the trend more clearly.
Calculating Chirps per 10 Seconds Using the data, we can observe that as the temperature increases, the average time between chirps decreases. This means the chirps occur more frequently. We can also calculate the number of chirps in 10 seconds for each day:
Day 1: 10/2.5 = 4.0 chirps Day 2: 10/2.6 ≈ 3.85 chirps Day 3: 10/2.2 ≈ 4.55 chirps Day 4: 10/2.3 ≈ 4.35 chirps Day 5: 10/2.0 = 5.0 chirps Day 6: 10/1.8 ≈ 5.56 chirps Day 7: 10/1.9 ≈ 5.26 chirps Day 8: 10/1.8 ≈ 5.56 chirps Day 9: 10/1.4 ≈ 7.14 chirps Day 10: 10/1.2 ≈ 8.33 chirps Day 11: 10/1.5 ≈ 6.67 chirps Day 12: 10/1.1 ≈ 9.09 chirps
As the temperature increases, the number of chirps in 10 seconds generally increases.
Determining the Relationship Since the average time between chirps decreases as the temperature increases, the chirps occur closer together. This also means that the number of chirps in a given time period (e.g., 10 seconds) increases as the temperature increases.
Confirming with Correlation Coefficient The data shows a strong negative correlation between temperature and the average time between chirps. The correlation coefficient is approximately -0.958. This confirms that as the temperature increases, the average time between chirps decreases, meaning the chirps occur closer together.
Final Answer Based on the analysis, the correct generalization is: The chirps occur closer together as the temperature increases.
Examples
Understanding the relationship between temperature and cricket chirp rates can be applied in ecological studies. For example, scientists can use cricket chirps as a natural thermometer to estimate the temperature of an environment. This can be useful in remote areas where weather instruments are not available. Also, this principle can be used in agriculture to monitor environmental conditions affecting insect behavior, which can impact crop health.
The data suggests that as the temperature increases, the average time between cricket chirps decreases, indicating that the chirps occur more frequently. Therefore, the best generalization is that the chirps occur closer together as the temperature increases. This corresponds to option B.
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