Let C = C(t) be the amount of chemical in a lake at time t in years. The amount of chemical is decreasing at a rate of 40% per year.

a) Three Math 1106 students are discussing the differential equation for the system. Chloe claims the equation is C = 0.4. Emma claims the equation is C = 0.4C. Sydney claims the equation is C = 0.6C. Who is correct? Explain why.

b)Suppose that when t = 0 there is 1000g of the chemical in the lake. Find the solution to all three differential equations from part a).

c) What will be the amount of chemical in the lake in 5 years. Answer for all three solutions you found in part b).

d) The lake will be safe to swim in once there is less than 50g of the chemical in it, when will that happen? Answer for all three solutions you found in part b) if possible.