(1 point) The population P of some species in an environment with limited resources is usually modelled by the logistic function 1 be-ct where a, b, c are positive constants and t represents time. It is known that the initial population is 155 and increases to 196 after 2 years. After a long time, the population will approach to the carrying capacity of 1070. (a) Find a, b and c so that the logistic equation P can be used to model the population of this species after t years. Round your answers to at least 5 significant figures. a= (b) What is the initial growth rate? Round your answer to at least 3 significant figures. Growth rate = /year (c) How long does it take for the population to reach 62% of the carrying capacity? Round your answer to at least 3 significant figures. It takes years.
(b) Use the logistic model to estimate the world population in the year 2000. Compare with the actual population of 6.1 billion. (Round the answer to two decimal places.) P =
(c) Use the logistic model to predict the world population in the years 2100 and 2500. (Round your answer to two decimal places.)
(d) What are your predictions if the carrying capacity is 60 billion? (Round your answers to two decimal places.)