An organism has a development time of t days at a

Question

Question: An organism has a development time of T days at a temperature H = f(t)°C. The total the number of degreedays S required for development to maturity is a constant defined by

S = ₀∫^T (f(t) - H_min) dt

(a) Evaluate this integral for T = 18, f(t) = 30°C, and Hmin = 10°C. What are the units of S?

(b) Illustrate this definite integral on a graph. Label the features corresponding to T , f(t), Hmin, and S.

(c) Now suppose H = g(t) = 20 + 10 cos(2πt/6)°C. Assuming that S remains constant, write a definite integral which determines the new development time, T₂. Sketch a graph illustrating this new integral. Judging from the graph, how does T₂ compare to T_? Find T₂.