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The effectiveness of an anesthetic t minutes after entering the blood stream is given by: e(t) = 2/25 ( 5 + 3t + 3t^2 – t^3) (a)
find the average rate of change of the drug effectiveness between t = 1 and t = 4 (b) find the instantaneous rates of change of the drug effectiveness at time = 1 and at time = 4. in one sentence, interpret the meaning of this value.
 one year ago
 one year ago
The effectiveness of an anesthetic t minutes after entering the blood stream is given by: e(t) = 2/25 ( 5 + 3t + 3t^2 – t^3) (a) find the average rate of change of the drug effectiveness between t = 1 and t = 4 (b) find the instantaneous rates of change of the drug effectiveness at time = 1 and at time = 4. in one sentence, interpret the meaning of this value.
 one year ago
 one year ago

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ganeshie8Best ResponseYou've already chosen the best response.0
average rate of change between [1,4] = \[\left[ e(4)  e(1) \right] / \left[ 4  1 \right]\]
 one year ago

soccergal12Best ResponseYou've already chosen the best response.0
By using that, would i get 6/25 as my answer?
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.0
thats correct for average rate of change. you have edited the question... now the question is talking about instantaneous rates of change, you need to use derivatives for (b)
 one year ago

soccergal12Best ResponseYou've already chosen the best response.0
yes, i used the derivatives and go the answers, on number is negative and the other is positive. it says to interpret the meaning of this value. what would i say?
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.0
that means, between t =1 and t =4, the anesthetic is becoming 0. and the patient gets up... makes sense ?
 one year ago

soccergal12Best ResponseYou've already chosen the best response.0
yeah! that does. thanks a lot :)
 one year ago

soccergal12Best ResponseYou've already chosen the best response.0
one more question. would the answers need units?
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.0
hey hold on. it doesnt mean that at all lol.. it means this : between t =1 and t =4, the anesthetic effect stopped INCREASING, became zero, and starts DECREASING. patient may not get up yet.. understood ? no units in the question right. so no need to bother, but if you wanto guess, the time must be in hours. as seconds are too small. and days are too long...
 one year ago

ganeshie8Best ResponseYou've already chosen the best response.0
after t= 4, patient may be lying unconscious, but the anesthetic effect has started decreasing some time ago after t=1.. hope it is clear
 one year ago

soccergal12Best ResponseYou've already chosen the best response.0
haha, yes. that makes sense. thanks again.
 one year ago
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