The population Pa of insect A after t years is given by the equation Pa = 1.3(1-0.038)^t while the population Pb of insect B after t years is Pb = 2.1(1-0.046)^t
We equate the above expressions to find the number of years t it will take the two populations to be equal: Pa = Pb 1.3(1-0.038)^t = 2.1(1-0.046)^t 1.3(0.962)^t = 2.1(0.954)^t These are the equations that can be used to determine how long it will be before the populations of the two species are equal.
We can now solve for t: (0.962)^t / (0.954)^t = 2.1/1.3 (0.962/0.954)^t = 2.1/1.3 After taking the log of both sides of our equation, number of years t is t = log (2.1/1.3) / log (0.962/0.954) t = 57 years Therefore, it will take 57 years for the population of insect A to equal the population of insect B.
