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Answer :
To predict the temperature based on cricket chirps per minute, one can use a linear model where the temperature is expected to have a relationship with the number of chirps. Here’s a step-by-step solution for predicting the temperature when crickets chirp at 1250 and 3000 times per minute:
1. Understand the Relationship:
- The relationship between the number of cricket chirps per minute and temperature is typically linear. This means as the chirps increase, the temperature tends to increase as well.
2. Model Assumptions:
- Assume a simple linear formula:
[tex]\[
\text{Temperature} = a \times \text{chirps} + b
\][/tex]
- In this instance:
- [tex]\(a\)[/tex] is the rate at which temperature changes per chirp.
- [tex]\(b\)[/tex] is the baseline temperature when there are 0 chirps.
3. Given Model:
- Coefficient values:
- [tex]\(a = 0.02\)[/tex] degrees per chirp
- [tex]\(b = 40\)[/tex] degrees (base temperature)
4. Calculate Temperature for 1250 Chirps/Minute:
- Substitute chirps per minute into the linear equation:
[tex]\[
\text{Temperature} = 0.02 \times 1250 + 40
\][/tex]
- Compute the result:
- Calculate [tex]\(0.02 \times 1250 = 25\)[/tex]
- Add [tex]\(40\)[/tex] to [tex]\(25\)[/tex] to get [tex]\(65\)[/tex] degrees.
5. Calculate Temperature for 3000 Chirps/Minute:
- Substitute chirps per minute into the linear equation:
[tex]\[
\text{Temperature} = 0.02 \times 3000 + 40
\][/tex]
- Compute the result:
- Calculate [tex]\(0.02 \times 3000 = 60\)[/tex]
- Add [tex]\(40\)[/tex] to [tex]\(60\)[/tex] to get [tex]\(100\)[/tex] degrees.
Predicted Temperatures:
- For 1250 chirps per minute, the predicted temperature is 65 degrees.
- For 3000 chirps per minute, the predicted temperature is 100 degrees.
These predictions are based on the assumed linear model coefficients.
1. Understand the Relationship:
- The relationship between the number of cricket chirps per minute and temperature is typically linear. This means as the chirps increase, the temperature tends to increase as well.
2. Model Assumptions:
- Assume a simple linear formula:
[tex]\[
\text{Temperature} = a \times \text{chirps} + b
\][/tex]
- In this instance:
- [tex]\(a\)[/tex] is the rate at which temperature changes per chirp.
- [tex]\(b\)[/tex] is the baseline temperature when there are 0 chirps.
3. Given Model:
- Coefficient values:
- [tex]\(a = 0.02\)[/tex] degrees per chirp
- [tex]\(b = 40\)[/tex] degrees (base temperature)
4. Calculate Temperature for 1250 Chirps/Minute:
- Substitute chirps per minute into the linear equation:
[tex]\[
\text{Temperature} = 0.02 \times 1250 + 40
\][/tex]
- Compute the result:
- Calculate [tex]\(0.02 \times 1250 = 25\)[/tex]
- Add [tex]\(40\)[/tex] to [tex]\(25\)[/tex] to get [tex]\(65\)[/tex] degrees.
5. Calculate Temperature for 3000 Chirps/Minute:
- Substitute chirps per minute into the linear equation:
[tex]\[
\text{Temperature} = 0.02 \times 3000 + 40
\][/tex]
- Compute the result:
- Calculate [tex]\(0.02 \times 3000 = 60\)[/tex]
- Add [tex]\(40\)[/tex] to [tex]\(60\)[/tex] to get [tex]\(100\)[/tex] degrees.
Predicted Temperatures:
- For 1250 chirps per minute, the predicted temperature is 65 degrees.
- For 3000 chirps per minute, the predicted temperature is 100 degrees.
These predictions are based on the assumed linear model coefficients.
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