The formula D = 36 m^−1.14 is sometimes used to determine the ideal population density D (individuals per square kilometer) for a large animal of mass m kilograms (kg).

a. What is the ideal population density for humans, assuming that a typical human weighs about 70 kg?

b. The area of the United States is about 9.2 million square kilometers. What would the population of the United States have to be for the population density to be ideal?

c. Consider an island of area 3,000 km². Two hundred animals of mass m = 30 kg are brought to the island, and t years later, the population is given by P(t) = 0.43t² + 13.37t + 200 How long does it take for the ideal population density to be reached? At what rate is the population changing when the ideal density is attained?