A 5-year projection of population trends suggests that t years from now, the population of a certain community will be $P ( t ) = - t ^ { 3 } + 12 t ^ { 2 } + 144 t + 50$ 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?

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The Answer of A 5-year projection of population trends suggests that t years from now, the population of a certain community will be $P ( t ) = - t ^ { 3 } + 12 t ^ { 2 } + 144 t + 50$ 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 5-Year Projection of Population Trends Suggests That T Years P(t)=−t3+12t2+144t+50P ( t ) = - t ^ { 3 } + 12 t ^ { 2 } + 144 t + 50P(t)=−t3+12t2+144t+50

A 5-Year Projection of Population Trends Suggests That T Years $P ( t ) = - t ^ { 3 } + 12 t ^ { 2 } + 144 t + 50$