The projected year-end assets in a particular trust fund, in trillions of dollars, where t represents the number of years since 2000, can be approximated by

A(t)=0.0000329t30.00450t2+0.061t+2.43,where0t50. Answer the following questions.

a. Find the value of A'(t).

b. Find the value of A''(t).

c. Find all the inflection points.

d. Find the value of t where the assets will decrease most rapidly.

e. Approximately when does this occur?