Question

The table below shows the average amount of time spent per person on entertainment per year from 2000 to 2005.Year Hours2000 34922001 35402002 36062003 36632004 37572005 3809(a) Use a graphing calculator or spreadsheet program to find a quadratic model that best fits this data. Let t represent the year, with t=0 in 2000. Round each coefficient to two decimal places.Pt =(b) Based on this model, how many hours would you expect the average person to spend on entertainment in 2012? Round your answer to the nearest whole number.hours(c) When would you expect the average amount of entertainment time to reach 4000? Give your answer as a calendar year (ex: 1997).During the year

Answer 1

EXPLANATION

Given the table,

Year Hours

2000 3492

2001 3540

2002 3606

2003 3663

2004 3757

2005 3809

Plugging in the data into a graphing calculator with a quadratic regression model AX^2+BX+C:

The function is:

P(t) = 2.35714 X^2 -9376.16 X +9325921.701

B)

When the time is 2012 substituting on the function:

P(t) = 2.357*(2012)^2 - 9,374.84*(2012) + 9.3246X10^6 = 3897.32

Hence, the number of hours spent in 2012 would be 3897 hours.

C) By using the graph, we can expect that the average amount of entertainment time to reach 4000 would be 9,540,465 hours.