3. A cell site is a site where electronic communications equipment is placed in a cellular network for the use of mobilephones. The numbers of cell sites from 1985 through 2011 can be modeled by269,573y :1+ 985e-0.308t=Where t represents the year, with t = 5 corresponding to 1985.Use the model to find the numbers of cell sites in the years 1998, 2003, and 2006.a.b. Use a graphing utility to graph the functionс.Determine the year in which the number of cell sites reached 250,000.

a. The given model is y=2695731+985e-0.308t, where t=5 corresponds to the year 1985. Note that, 1998-1985=13 and 1985 corresponds to t=5. To find the number of cell sites in the year 1998, substitute t=18 (13+5) in y=2695731+985e-0.308t. y=2695731+985e-0.30818=55556.98309…≈55556.98 Thus, the number of cell sites in the year 1998 is 55556.98. Note that, 2003-1985=18 and 1985 corresponds to t=5. To find the number of cell sites in the year 2003, substitute t=23 (18+5) in y=2695731+985e-0.308t. y=2695731+985e-0.30823=147643.55232…≈147643.55 Thus, the number of cell sites in the year 2003 is 147643.55. Note that, 2006-1985=21 and 1985 corresponds to t=5. To find the number of cell sites in the year 2006, substitute t=26 (21+5) in y=2695731+985e-0.308t. y=2695731+985e-0.30826=203022.63063…≈203022.63 Thus, the number of cell sites in the year 2006 is 203022.63.b. Use Desmos graphing calculator and sketch the graph as follows.c. Determine the year in which the number of site cells reaches 250000 as follows. 250000=2695731+985e-0.308t1+985e-0.308t=269573250000985e-0.308t=269573250000-1e-0.308t=0.078292985ln e-0.308t=ln 0.00007-0.308t=-9.56701t=-9.56701-0.308t=31.06172t≈31 Note that, t=5 corresponds to 1985. Then, 31-5=26 and 1985+26=2011. Thus, the year in which the number of site cells reaches 250000 is 2011.