10 **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.

Answered: Image /qna-images/answer/eff9c9bb-7f8c-4503-96ae-c6236d70e586.jpg

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? $

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

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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