Question 1131149
During surgery, a patient's circulatory system requires at least 50 milligrams of an anesthetic. The amount of anesthetic present t hours after 70 milligrams of anesthetic is administered is given by the following.


{{{T(t) = 70(0.727)^t}}}

(a) How much, to the nearest milligram, of the anesthetic is present in the patient's circulatory system {{{t=20}}} minutes after the anesthetic is administered_______mg

{{{20}}} minutes is (1/3) hour, so evaluate T for t=(1/3)

{{{T(1/3) = 70(0.727)^(1/3)}}}

{{{T(1/3) = 70*root(3,0.727)}}}
{{{T(1/3) = 70*0.899176}}}

{{{T(1/3) = 62.94232}}}

to the nearest milligram:

{{{T(1/3) = 63mg}}}


b) How long, to the nearest minute, can the operation last if the patient does not receive additional anesthetic?_______min

{{{63 = 70(0.727)^t}}}

{{{63/ 70=(0.727)^t}}}

{{{0.9=(0.727)^t}}}

{{{log(0.9)=log((0.727)^t)}}}

{{{log(0.9)=tlog(0.727)}}}

{{{t=log(0.9)/log(0.727)}}}

{{{t=0.330461}}} hours

{{{t=0.330461hours* 60 (min/hour)}}}

{{{t=19.8277min}}}=> {{{t=20min}}}