Question: The amount of land in use for growing crops increases as the world's population increases. Suppose A(t) represents the total number of hectares of land in use in year t. (A hectare is about 2½ acres.)
(a) Explain why it is plausible that A(t) satisfies the equation A' (t) = kA(t). What assumptions are you making about the world's population and its relation to the amount of land used?
(b) In 1966 about 4.55 billion hectares of land were in use; in 1996 the figure was 4.93 billion hectares. If the total amount of land available for growing crops is thought to be 6 billion hectares, when does this model predict it will be exhausted? (Let t = 0 in 1966.)