Bushfires have recently caused much devastation to natural habitats of rare Australian Animals. The Silver-headed Antechinus in South-east Queensland is a case in point. The Silver-headed Antechinus Population (P) is modelled by the differential equation dP dt = -0.025 (PM) Where: t is the number of years that has passed since 2019 and M is an upper bound on the population due to lack of resources. The Government has pledged a money grant if M is less than 10 000 to help improve the environment for the Silver-headed Antechinus. (a) Use the separation of variables technique to formulate a solution to the differential equation. (b) In 2019, there were 2300 Silver-headed Antechinus and in 2022 there were 2650. Determine whether or not a government grant will be given.