A 5-Year Projection of Population Trends Suggests That T Years $P ( t ) = - t ^ { 3 } + 15 t ^ { 2 } + 72 t + 55$

Multiple Choice

A 5-year projection of population trends suggests that t years from now,the population of a certain community will be $P ( t ) = - t ^ { 3 } + 15 t ^ { 2 } + 72 t + 55$ thousand.
a.At what time during the 5-year period will the population be growing most rapidly?
b. At what time during the 5-year period will the population be growing least rapidly?
c. At what time is the rate of population growth changing most rapidly?

A) a.t = 2 yearsb.t = 0 yearsc.t = 2 years
B) a.t = 2 yearsb.t = 1 yearc.t = 3 years
C) a.t = 5 yearsb.t = 0 yearsc.t = 0 years
D) a.t = 0 yearsb.t = 0 yearsc.t = 2 years