We appreciate your visit to The function tex f t 349 2 0 98 t tex models the relationship between tex t tex the time an oven spends cooling and. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To solve this question, we need to determine which temperature most accurately matches the modeled prediction for a specific cooling time using the function [tex]\( f(t) = 349.2 \times (0.98)^t \)[/tex]. This function models the relationship between [tex]\( t \)[/tex], the time in minutes, and the oven temperature [tex]\( f(t) \)[/tex].
Here's how we can approach the solution step by step:
1. Calculate Temperature for Each Time: Use the given function to calculate the oven temperature for each of the cooling times provided (5, 10, 15, 20, and 25 minutes).
2. Compare Calculated Temperatures with Given Data: Compare the modeled temperatures for each time with the provided temperatures in the chart to determine how accurately the function predicts each measured temperature.
3. Identify Temperature With Smallest Difference: For each time, calculate the difference between the modeled temperature and the given temperature. The goal is to find the smallest difference, which indicates the most accurate prediction.
- At 5 minutes:
- Modeled: [tex]\( 349.2 \times (0.98)^5 \)[/tex]
- Given: 315°F
- At 10 minutes:
- Modeled: [tex]\( 349.2 \times (0.98)^{10} \)[/tex]
- Given: 285°F
- At 15 minutes:
- Modeled: [tex]\( 349.2 \times (0.98)^{15} \)[/tex]
- Given: 260°F
- At 20 minutes:
- Modeled: [tex]\( 349.2 \times (0.98)^{20} \)[/tex]
- Given: 235°F
- At 25 minutes:
- Modeled: [tex]\( 349.2 \times (0.98)^{25} \)[/tex]
- Given: 210°F
4. Conclusion: By calculating the differences, we find that the temperature prediction for 10 minutes (approximately 285.32°F) is the most accurate, closely matching the given temperature of 285°F.
Thus, the temperature for which the model most accurately predicts the time spent cooling is 285°F.
Here's how we can approach the solution step by step:
1. Calculate Temperature for Each Time: Use the given function to calculate the oven temperature for each of the cooling times provided (5, 10, 15, 20, and 25 minutes).
2. Compare Calculated Temperatures with Given Data: Compare the modeled temperatures for each time with the provided temperatures in the chart to determine how accurately the function predicts each measured temperature.
3. Identify Temperature With Smallest Difference: For each time, calculate the difference between the modeled temperature and the given temperature. The goal is to find the smallest difference, which indicates the most accurate prediction.
- At 5 minutes:
- Modeled: [tex]\( 349.2 \times (0.98)^5 \)[/tex]
- Given: 315°F
- At 10 minutes:
- Modeled: [tex]\( 349.2 \times (0.98)^{10} \)[/tex]
- Given: 285°F
- At 15 minutes:
- Modeled: [tex]\( 349.2 \times (0.98)^{15} \)[/tex]
- Given: 260°F
- At 20 minutes:
- Modeled: [tex]\( 349.2 \times (0.98)^{20} \)[/tex]
- Given: 235°F
- At 25 minutes:
- Modeled: [tex]\( 349.2 \times (0.98)^{25} \)[/tex]
- Given: 210°F
4. Conclusion: By calculating the differences, we find that the temperature prediction for 10 minutes (approximately 285.32°F) is the most accurate, closely matching the given temperature of 285°F.
Thus, the temperature for which the model most accurately predicts the time spent cooling is 285°F.
Thanks for taking the time to read The function tex f t 349 2 0 98 t tex models the relationship between tex t tex the time an oven spends cooling and. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
