Exercise 1.3.107: apopulation x of rabbits on an island is modeled by x x- (/1000)x, where the independent variable is time in months. at time t = 0, there are 40 rabbits on the island. a) find the solution to the equation with the initial condition. b) how many rabbits are on the island in 1 month, 5 months, 10 months, 15 months (round to the nearest integer) =

So the first thing we do is to multiply the top equation by 3. the reason i want to do this is i notice there will be a 6y on both equations and can possibly add/subtract them. so we get 6y = -3x + 27. adding that and the second equation we get 6x = 27-15 which is 12. divide by 6 and we get 2. ∴ x = 2. substituting 2 into the first equation we get 2y = -2 + 9 which is 7. divide by 2 and we get 7/2. ∴ y = 7/2, x = 2.