Question

A conservation organization released 100 animals of an endangered species into a game preserve. The preserve has a carrying capacity of 800 animals. The growth of the pack is modeled by the logistic curve 800 p(t) = 1 + 7e-0.16987 where t is measured in months (see figure). 12001 1000 LLLLLLLLL 800 600 400 200 TILILI 5 10 15 20 (a) Estimate the population after 8 months. (Round your answer to the nearest whole number.) animals (b) After how many months is the population 700? (Round your answer to the nearest whole number.) months (c) Use a graphing utility to graph the function. Use the graph to determine the horizontal asymptotes. (smaller value) (larger value)

Answer 1

PCH = 80201698t -0.4690t (+7e @ after 8 möths t=8 - 800 PCO) = 1:350 ooo 1+72-0.169000) pol Doo - = 285-765 2.7995 1206 J animals, population 700 700-000 -0.1690t +ye it 7e-0016986 - Q 76 -0.1698 in 720-1898€ = 4 ence 01698+) = ln (ta) -001690t encel=en (4) t = encual = 22.92 -0.1698 to 23 123months Tences V Horizontal asymptote p= o smaller. p = 70oo larger Scanned with CamScanner

& Hlde Plor Plotting: - 800 1 + 7e-0.16957 View Larger 2000 1500 1000 5001 -60 40 -300