The following table provides the land area in Australia colonized by the American marine...

The following table provides the land area in Australia colonized by the American marine toad (Bufo marinas) every five years from 1939-1974. Model the migration of this toad using an exponential growth model

where in this case A(t) is the land area occupied at tithe t. Make predictions about the land area occupied in the years 2010, 2050, and 2100. You should do this by

(a) solving the initial-value problem,

(b) determining the constant k,

(c) computing the predicted areas, and

(d) comparing your solution to the actual data. Do you believe your prediction?

(Note that there are many exponential growth models that you can form using this data. Is one a more reasonable model than the others? Note also that the area of Queensland is 1,728,000 km2 and the area of Australia is 7,619,000 km².)*

Remark: The American marine toad was introduced to Australia to control sugar cane beetles and, in the words of J. W. Hedgpath (see Science, July 1993 and The New York Times, July 6, 1993),

Unfortunately the toads are nocturnal feeders and the beetles are abroad by day, while the toads sleep under rocks, boards and burrows. By night the toads flourish, reproduce phenomenally well and eat up everything they can find. The cane growers were warned by Walter W. Froggart, president of the New South Wales Naturalist Society, that the introduction was not a good idea and that the toads would eat the native ground fauna. He was immediately denounced as an ignorant meddlesome crank. He was also dead right.