James bought a puppy and has been tracking its weight at the end of each month since it was born. He was told by the dog's breeder that the dog should have an adult weight somewhere between 45 and 50 pounds. End of Month 1 2 3 4 5 6 7 8 9 10 11 12 Weight (in pounds) 2 5 9 14 19 22 27 32 37 42 44 46 Step 1 of 2: The quadratic function w(t) = -0.036t2 +4.754t - 4.023 models the weight of the puppy after t months. By this model, what is the extrapolated weight of the dog after 3 years? Round your answer to the nearest pound.
James bought a puppy and has been tracking its weight at the end of each month since it was born. He was told by the dog's breeder that the dog should have an adult weight somewhere between 45 and 50 pounds. End of Month 1 2 3 4 5 6 7 8 9 10 11 12 Weight (in pounds) 2 5 9 14 19 22 27 32 37 42 44 46 Step 1 of 2: The quadratic function w(t) = -0.036t2 +4.754t - 4.023 models the weight of the puppy after t months. By this model, what is the extrapolated weight of the dog after 3 years? Round your answer to the nearest pound.
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
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Transcribed Image Text:James bought a puppy and has been tracking its weight at the end of each month since it was born. He was told by the dog's breeder that the dog should have an adult weight somewhere between 45 and 50 pounds.
### Weight Tracking Table
| End of Month | Weight (in pounds) |
|--------------|--------------------|
| 1 | 2 |
| 2 | 5 |
| 3 | 9 |
| 4 | 14 |
| 5 | 19 |
| 6 | 22 |
| 7 | 27 |
| 8 | 32 |
| 9 | 37 |
| 10 | 42 |
| 11 | 44 |
| 12 | 46 |
### Mathematical Analysis
**Step 1 of 2:**
The quadratic function \( w(t) = -0.036t^2 + 4.754t - 4.023 \) models the weight of the puppy after \( t \) months. By this model, what is the extrapolated weight of the dog after 3 years? Round your answer to the nearest pound.
### Explanation
This table lists the weight of the puppy at the end of each month for its first year. The quadratic function provided helps to model and predict the puppy's weight over time, offering insights into its growth pattern. By analyzing the table, one can see a gradual increase in weight, aligning with the breeder's expectations for adult weight. The task is to predict the weight at 36 months using the given quadratic equation.
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