Buffalo: Waterton Lakes National Park of Canada, where the Great Plains dramatically meet the Rocky Mountains in Alberta, has a migratory buffalo (bison) herd that spends falls and winters in the...

Buffalo: Waterton Lakes National Park of Canada, where the Great Plains dramatically meet the Rocky Mountains in Alberta, has a migratory buffalo (bison) herd that spends falls and winters in the park. The herd is currently managed and so kept small; however, if it were unmanaged and allowed to grow, then the number N of buffalo in the herd could be estimated by the logistic formula

Here t is the number of years since the beginning of 2002, the first year the herd is unmanaged.

a. Make a graph of N versus t covering the next 30 years of the herd’s existence (corresponding to dates up to 2032).

b. How many buffalo are in the herd at the beginning of 2002?

c. When will the number of buffalo first exceed 300?

d. How many buffalo will there eventually be in the herd?

e. When is the graph of N , as a function of t, concave up? When is it concave down? What does this mean in terms of the growth of the buffalo herd?