Based on data from 298 of 351 cities and towns in Massachusetts, the average single-family property tax bill from 1997 through 2007 is approximated by the function T(t) = 7.26t² + 91.7t + 2360 (0 ≤ t ≤ 10) where T(t) is measured in dollars and t in years, with t = 0 corresponding to 1997.† (a) What was the average property tax on a single-family home in Massachusetts in 2001? $ (b) If the trend continued, what was the average property tax in 2008? $
Based on data from 298 of 351 cities and towns in Massachusetts, the average single-family property tax bill from 1997 through 2007 is approximated by the function T(t) = 7.26t² + 91.7t + 2360 (0 ≤ t ≤ 10) where T(t) is measured in dollars and t in years, with t = 0 corresponding to 1997.† (a) What was the average property tax on a single-family home in Massachusetts in 2001? $ (b) If the trend continued, what was the average property tax in 2008? $
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Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Property Tax Analysis in Massachusetts: 1997-2007**
Based on data from 298 of 351 cities and towns in Massachusetts, the average single-family property tax bill from 1997 through 2007 is approximated by the function:
\[ T(t) = 7.26t^2 + 91.7t + 2360 \qquad (0 \le t \le 10) \]
where \( T(t) \) is measured in dollars and \( t \) in years, with \( t = 0 \) corresponding to 1997.
### Questions
**(a) What was the average property tax on a single-family home in Massachusetts in 2001?**
\[ \text{Answer: } \$ \square \]
**(b) If the trend continued, what was the average property tax in 2008?**
\[ \text{Answer: } \$ \square \]
### Explanation
- The function \( T(t) \) represents the property tax amount in dollars as a function of time \( t \), with \( t = 0 \) indicating the starting year, 1997.
- The quadratic equation \( 7.26t^2 + 91.7t + 2360 \) includes:
- A quadratic term \( 7.26t^2 \) which implies an accelerating increase in tax over time,
- A linear term \( 91.7t \),
- A constant term 2360 representing the initial property tax amount in 1997.
To solve the given questions:
1. Calculate the property tax in 2001 (\( t = 4 \)) by substituting \( t = 4 \) into the equation.
2. For the year 2008 (\( t = 11 \)), substitute \( t = 11 \) into the function to predict the tax, despite the function being explicitly given for \( 0 \le t \le 10 \).
Graphical or numerical approximations may be used for validation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8eeb6921-a110-4984-a04e-b3e01fc97c1d%2Feff9c9bb-7f8c-4503-96ae-c6236d70e586%2Frmp4cf8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Property Tax Analysis in Massachusetts: 1997-2007**
Based on data from 298 of 351 cities and towns in Massachusetts, the average single-family property tax bill from 1997 through 2007 is approximated by the function:
\[ T(t) = 7.26t^2 + 91.7t + 2360 \qquad (0 \le t \le 10) \]
where \( T(t) \) is measured in dollars and \( t \) in years, with \( t = 0 \) corresponding to 1997.
### Questions
**(a) What was the average property tax on a single-family home in Massachusetts in 2001?**
\[ \text{Answer: } \$ \square \]
**(b) If the trend continued, what was the average property tax in 2008?**
\[ \text{Answer: } \$ \square \]
### Explanation
- The function \( T(t) \) represents the property tax amount in dollars as a function of time \( t \), with \( t = 0 \) indicating the starting year, 1997.
- The quadratic equation \( 7.26t^2 + 91.7t + 2360 \) includes:
- A quadratic term \( 7.26t^2 \) which implies an accelerating increase in tax over time,
- A linear term \( 91.7t \),
- A constant term 2360 representing the initial property tax amount in 1997.
To solve the given questions:
1. Calculate the property tax in 2001 (\( t = 4 \)) by substituting \( t = 4 \) into the equation.
2. For the year 2008 (\( t = 11 \)), substitute \( t = 11 \) into the function to predict the tax, despite the function being explicitly given for \( 0 \le t \le 10 \).
Graphical or numerical approximations may be used for validation.
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