The rational function $M ( t ) = \frac { 0.5 t + 150 } { 0.04 t ^ { 2 } + 3 }$ models the number of milligrams of medication in the bloodstream of a patient t hours after 150 milligrams of the medication have been injected into the patient's bloodstream. What will M approach as $t \rightarrow \infty$ ?
A)13 mg
B)6 mg
C)50 mg
D)0 mg
E)9 mg

Question

Quizplus · Accepted Answer

As $t \rightarrow \infty$, the denominator of $M(t)$ will approach infinity much faster than the numerator. Therefore, $M(t)$ will approach 0.

The Rational Function M(t)=0.5t+1500.04t2+3M ( t ) = \frac { 0.5 t + 150 } { 0.04 t ^ { 2 } + 3 }M(t)=0.04t2+30.5t+150​

The Rational Function $M ( t ) = \frac { 0.5 t + 150 } { 0.04 t ^ { 2 } + 3 }$