$\text { A population is growing according to the logistic model } N = \frac { 6000 } { 1 + e ^ { 4.2 - 1.6 ^ { t } } } \text {, where } t$

$\text { A population is growing according to the logistic model } N = \frac { 6000 } { 1 + e ^ { 4.2 - 1.6 ^ { t } } } \text {, where } t$ is the time in days. Find the average population over the interval $[ 0,2 ]$ . Round your answer to one decimal place.

A) $559.5 \mathrm { ft } . \mathrm { lbs }$
B) $2434.5 \mathrm { ft }$ lbs
C) $716.1 \mathrm { ft } \mathrm { lbs }$
D) $5117.6 \mathrm { ft } . \mathrm { lbs }$
E) $3116.1 \mathrm { ft }$ lbs