Question

A species of fish was added to a lake. The population size P (t) of this species can be modeled by the following exponential function, where t is the number of years from the time the species was added to the lake.P (t) =1000/(1+9e^0.42t) Find the initial population size of the species and the population size after 9 years. Round your answer to the nearest whole number as necessary. Initial population size is : Population size after 9 years is:

Answer 1

Given: The function can model the population size P(t) of the fishes

where t is the time

We have to find the initial population size

Initial population size is number of fishes when fishes are added in pond

and is given when t = 0 That is P(0)

and after 9 years, the population size will be given by function P(9)

THUS, INITIAL POPULATION SIZE IS 100 FISHES

AND POPULATION SIZE AFTER 9 YEARS WILL BE 830 FISHES.