Surds and Indices

Question

Fenitoine is administered intravenously through a bolus injection. The concentration, C µg/ml , of the drug in the blood, t hours after administration is given by C=4.86e^-0047t .

State the concentration as t becomes very large.

 

Ans: 0µg/ml

 

Thank You! :)

Answer 1

Let's rewrite the formula so that it visually makes more sense to us.  We'll rewrite the exponent such that the formula is:

 

                   1

                -------

               .0047t

C = 4.86e

 

Rewriting the formula shows that the independent variable t is in the denominator of the exponent.  This means that as t gets larger, the exponent as a whole gets smaller, and thus C gets smaller.  Plugging in numbers shows this.  We generate some coordinates (1, 1.2x10^93) (24, 3.4x10^4) (48, 409) and observe that the C value is dropping very quickly as t increases.  Therefore at some very large number, C essentially becomes zero (though it never technically gets to zero).

 

I'm not sure which course you are enrolled in, but to explain it another way, in (pre)calculus we would look at this as a limit problem.  The limit as t goes to infinity = 0.