4.2632The population P (in thousands) of a city from 2000 through 2010 can be modeled by P =1+0.083e0.050tWhere t represents the year, with t = 0 corresponding to 2000.Use the model to find the populations of the city in the years 2000, 2005 and 2010.a.b. Use a graphing utility to graph the function.с.Determine the year in which the population will reach 2.2 million.

The population of the city is given by the function P=26321+0.083e0.050t where t represents year, with t=0 corresponding to 2000. (a) For the year 2000, the value of t is 0. Evaluate the population of the city in the year 2000 as follows. P=26321+0.083e0.0500=26321+0.083=26321.083=2,430.2862 Therefore, the population of the city in the year 2000 is about 2,430,286.For the year 2005, the value of t is 5. Evaluate the population of the city in the year 2005 as follows. P=26321+0.083e0.0505=26321+0.10657=26321.10657=2378.51218 Therefore, the population of the city in the year 2005 is about 2,378,512. For the year 2010, the value of t is 10. Evaluate the population of the city in the year 2010 as follows. P=26321+0.083e0.05010=26321+0.13684=26321.13684=2315.1816 Therefore, the population of the city in the year 2010 is about 2,315,182.(b) Sketch the graph of the function as shown in the figure below. From the above graph, notice that the population is decreasing gradually.(c) It is given that the population is 2.2 million. So, the value of P is 2200 (as P is in thousand's). Evaluate the year in which the population will become 2.2 million as follows. P=26321+0.083e0.050t2200=26321+0.083e0.050t1+0.083e0.050t=263222000.083e0.050t=0.19636e0.050t=2.365780.050t=ln2.36578 Take logarithm on both sidest=0.861100.050t≈17.22 Thus, the population will become 2.2 million after 17 years. Therefore, the population will be 2.2 million in the year 2017.