The age/weight relationship of male Arctic foxes caught in Svalbard, Norway, can be estimated by the function M(t) = 3583e^{-e-0.020(t-66)}, where t is the age of the fox in days and M(t) is the weight of the fox in grams.

(a) Estimate the weight of a male fox that is 250 days old.
(b) Use M(t) to estimate the largest size that a male fox can attain.

(c) Estimate the age of a male fox when it has reached 50% of its maximum weight.

(d) Estimate the rate of change in weight of a male Arctic fox that is 250 days old.

(e) Use a graphing calculator to graph M(t) and then describe the growth pattern.
(f) Use the table function on a graphing calculator or a spreadsheet to develop a chart that shows the estimated weight and growth rate of male foxes for days 50, 100, 150, 200, 250, and 300.