1. Consider the differential equation _ _ =ky(10 - y) Lety =f (x) be the dx particular solution to the differential equation with the initial condition f (0) = 1 Part A: Use Euler's method with two steps of equal size to approximate (2) in terms of k. Part B: Find f"(0) in terms of k and y. 2. At the beginning of 2020, a manufacturer's warehouse contained 1,100 tons of product. The increasing function A models the total amount of material stored in the warehouse. Administration estimates that A will satisfy the differential equation "_ _ (A-100) for the next 10 years. A at 10 is measured in tons, and t is measured in years from the start of 2020. Part A: Use the line tangent to the graph of A at t = 0 to approximate the amount of product that the warehouse contains at the end of the first three months of 2020 (time ( = -). Show the work that leads to your answer. Part B: Find in terms of A. Use to determine whether your answer in part A is an underestimate or an overestimate of the amount M hp .............. .. . .............................. .. ................... ... ......................three months of 2020 (time ? - ). Show the work that leads to your answer. Part B: Find in terms of A. Use to determine whether your answer in part A is an underestimate or an overestimate of the amount of product that the warehouse contains at time {- -. Show the work that leads to your answer. Part C: Find the particular solution to the differential equation dA (4-100) with initial condition A(0)= 1100. Show the work that leads to your answer. np