The population y (in thousands) of Raleigh, North Carolina, from 2000 to 2014 can be approximated by the model y 11 09t 293 4, 0 curren t curren 14, where t represents the year, with t 0 corresponding to 2000 (see figure) (Source U S Census Bureau) (a) Graphically estimate the y intercept of the gr...

The population y (in thousands) of Raleigh, North Carolina, from 2000 to 2014 can be approximated by

Question:

The population y (in thousands) of Raleigh, North Carolina, from 2000 to 2014 can be approximated by the model y = 11.09t + 293.4, 0 ‰¤ t ‰¤ 14, where t represents the year, with
t = 0 corresponding to 2000 (see figure). (Source: U.S. Census Bureau)

460 440 420 400 ****** 380 360+ 340+ 320 300+ 280 ++++++++++++++ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Year (0 + 2000) Popula

(a) Graphically estimate the y-intercept of the graph.
(b) Find algebraically and interpret the y-intercept of the graph.
(c) Use the model to predict the year in which the population will be 538,000. Does your answer seem reasonable? Explain.