Question

21² + 6 Ay The population, P, in thousands of a resort community is given 100 600t by P(t) = t20, where t is time, in months. 80-A a) Find the population at t= 0, 1, 3, and 8 months. .60 b) Find the horizontal asymptote of the graph and determine the 401 value that P(t) approaches as t goes to co? c) Explain the meaning of the answer to part (b) in terms of the 20- application 0 10 20 30 40 51 0- a) Att=0, the population is At t= 1, the population is At t= 3, the population is At t= 8, the population is (Simplify your answers. Round to the nearest integer as needed.) b) Find any horizontal asymptotes. Select the correct choice below, and if necessary, fill int O A. The horizontal asymptote(s) is/are (Type an equation.) OB. The graph has no horizontal asymptote. Complete the following P(t) goes to as t goes to co (Type an integer or a decimal.) c) What does this indicate about the population? Choose the correct answer below. O A. In time, the population of this community decreases to 300. Click to select your answer(s).

Answer 1

in part b) if your computer gives wrong you can put the asymptote as p(t) = 0

p() = 600 t at +6 600x0 a) PLO) = 0 P(3) - = 75 2x 0 +6 1800 24 4800 134 600 P(1) - P(x) = Ž 36 2 +6 2:25 so as t=0, opmortion is o 75 at t = !, 10 an t N 75 را 1 at 28, t 12 36 b) 6oot P(t) = 2ť +6 6001t 2.46/ to aszt (A The horizontal asymptote is y=0 p(t) goes to as t goes too. 2 1 B In time, no one lives in this community.