The population (P) of an island y years after colonisation is given by the function
P = 250/(1+4e^-0.01y)
A. What was the initial population of the island?
B. How long did it take before the island had a population of 150?
C. After how many years was the population growing the fastest?
Water is leaking from a trough at the rate of 0.8 l/s. The trough has a trapezoidal cross section, where the width at the bottom is 55 cm, at the top is 85cm, and the height is 25 cm. The length of the trough is 3 m.
Find the rate at which the height is changing when the depth of water is 11 cm.