The game commission introduces 100 deer into newly acquired

The game commission introduces 100 deer into newly acquired state game lands. The population N of the herd is modeled by N = 20(5 + 3t) / 1 + 0.04t, t 0 where t is the time in years. Find the populations when t = 6, t = 10, and t = 20.

Solution

N = 20( 5 +3t)/( 1 +0.04t) for t>=0

a) t =6 find N

N = 20( 5 +3*6)/(1 +0.04*6)

= 370.96 = 371 deer

t= 10

N = 20(5 +3*10)/( 1 +0.04*10)

= 500 deer

t = 20

N = 20( 5 +3*20)/ ( 1 +0.04*20)

= 722.22 = 722 deer

b) As t ---> infinity N ---> 20*5/(0.04) ---> 1500 deer