Growth rates of insects depend on the temperature T. Suppose that the length of an insect L follows the differential equation
dL/dt = 0.001T(t)
with t measured in days starting from January 1 and temperature measured in °C. Insects hatch with an initial size of 0.1 cm. For each of the following equations for T(t),
a. Sketch a graph of the temperature over the course of a year.
b. Suppose an insect starts growing on January 1. How big will it be after 30 days?
c. Suppose an insect starts growing on June 1 (day 151). How big will it be after 30 days?
T(t) = 40.0 - 5.0 × 10-6t2(365 - t).