$\text { A calf that weighs } 80 \text { pounds at birth gains weight at the rate } \frac { d w } { d t } = k ( 1500 - w ) \text {, }$ where $w$ is weight in pounds and $t$ is time in years. What is the maximum weight of the animal if one uses the model $w = 1500 - 1420 e ^ { - 0.9 t }$ ?
A) $1500 \mathrm { lb }$
B) $880 \mathrm { lb }$
C) $1420 \mathrm { lb }$
D) $1580 \mathrm { lb }$
E) $2300 \mathrm { lb }$

Question

Quizplus · Accepted Answer

The maximum weight of the animal according to the given model $w = 1500 - 1420 e ^ { - 0.9 t }$ is achieved as $t$ approaches infinity, because the exponential term $1420 e ^ { - 0.9 t }$ approaches 0. Therefore, the maximum weight $w$ approaches $1500$ pounds.

A calf that weighs 80 pounds at birth gains weight at the rate dwdt=k(1500−w), \text { A calf that weighs } 80 \text { pounds at birth gains weight at the rate } \frac { d w } { d t } = k ( 1500 - w ) \text {, } A calf that weighs 80 pounds at birth gains weight at the rate dtdw​=k(1500−w),

$\text { A calf that weighs } 80 \text { pounds at birth gains weight at the rate } \frac { d w } { d t } = k ( 1500 - w ) \text {, }$