Chapter 1.2, Problem 70E

Population The population $y$ (in thousands) of Buffalo, New York, from $2000$ to $2014$ can be approximated by the model $y=-2.60t+291.7,0\le t\le 14,$ where $t$ represents the year, with $t=0$ corresponding to $2000$ (see figure).

(a) Graphically estimate the $y\text{-intercept}$ of the graph.

(b) Find algebraically and interpret the $y\text{-intercept}$ of the graph.

(c) Use the model to predict the year in which the population will be $239,000.$ Does your answer seem reasonable? Explain.