The daily milk consumption (in kilograms) for calves can be approximated by the function y = b₀w^b1e^{-b2 w}, where w is the age of the calf (in weeks) and b₀, b₁, and b₂ are constants.

(a) The age in days is given by t = 7w. Use this fact to convert the function above to a function in terms of t.

(b) For a group of Angus calves, b₀ = 5.955, b₁ = 0.233, and b₂ = 0.027. Use the trapezoidal rule with n = 10, and then Simpson’s rule with n = 10, to find the total amount of milk consumed by one of these calves over the first 25 weeks of life.

(c) For a group of Nelore calves, b₀ = 8.409, b₁ = 0.143, and b₂ = 0.037. Use the trapezoidal rule with n = 10, and then Simpson’s rule with n = 10, to find the total amount of milk consumed by one of these calves over the first 25 weeks of life.