The game commission introduces 100 deer into newly acquired state game lands.The population N of the herd is modeled by
$N = \frac { 24 ( 5 + 3 t ) } { 1 + 0.04 t } , t \geq 0$
Where t is the time in years.Find the populations when t = 40.
(Round your answer to the nearest whole number.)

A)1,154 deer
B)1,306 deer
C)1,275 deer
D)1,240 deer
E)1,200 deer

Question

The game commission introduces 100 deer into newly acquired state game lands.The population N of the herd is modeled by 
 $N = \frac { 24 ( 5 + 3 t ) } { 1 + 0.04 t } , t \geq 0$  
Where t is the time in years.Find the populations when t = 40.
(Round your answer to the nearest whole number.)
 
A)1,154 deer
B)1,306 deer
C)1,275 deer
D)1,240 deer
E)1,200 deer

Quizplus · Accepted Answer

The population when t = 40 is 1,154 deer.To find the population when t = 40, we substitute t = 40 into the given equation:$N = \frac { 24 ( 5 + 3 t ) } { 1 + 0.04 t } $$N = \frac { 24 ( 5 + 3 ( 40 ) ) } { 1 + 0.04 ( 40 ) } $$N = \frac { 24 ( 5 + 120 ) } { 1 + 1.6 } $$N = \frac { 24 ( 125 ) } { 2.6 } $$N = \frac { 3000 } { 2.6 } $$N = 1153.8461538461539 $Rounding to the nearest whole number, we get 1,154 deer.

The Game Commission Introduces 100 Deer into Newly Acquired State N=24(5+3t)1+0.04t,t≥0N = \frac { 24 ( 5 + 3 t ) } { 1 + 0.04 t } , t \geq 0N=1+0.04t24(5+3t)​,t≥0

The Game Commission Introduces 100 Deer into Newly Acquired State $N = \frac { 24 ( 5 + 3 t ) } { 1 + 0.04 t } , t \geq 0$