1a. Using data in a car magazine, we constructed the mathematical model y = 100e^-0.0482t for the percentage of cars of a certain type still on the road after tyears. Using Python, determine the rate of change of the percent of cars still on the road after 5 years.

1b. A patient takes vitamin pills daily. Each day he must have at least 240 IU of vitamin A, 5 mg of vitamin B₁, and 120 mg of vitamin C. He can choose between pill 1, which contains 120 IU of vitamin A, 1 mg of vitamin B₁, and 15 mg of vitamin C; and pill 2, which contains 30 IU of vitamin A, 1 mg of vitamin B₁, and 40 mg of vitamin C. Pill 1 costs $0.10, and pill 2 costs $0.20. Using Python, determine how many of each pill he should take daily in order to minimize cost and determine the minimum cost. Also, determine the amount of surplus of each type of vitamin, if any.