The population P (in thousands) of a colony of rabbits at time (t) years is given by P(t) = 3+ae−bt, t ≥0 where a and b are positive constants. If it is given that the initial population is 10,000 rabbits and one year later this population has reduced by 2,000, find the following; (a) The values of a and b.
since P(0) = 3 we have a = 9997,and so
P(t) = 3+9997e^(-bt)
Since P(1) = 8000,
3+997e^-b = 8000
b = ln(997/7997)