Question

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.

Answer 1

average rate of change between [1,4] = \[\left[ e(4) - e(1) \right] / \left[ 4 - 1 \right]\]

Answer 2

By using that, would i get -6/25 as my answer?

Answer 3

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)

Answer 4

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?

Answer 5

that means, between t =1 and t =4, the anesthetic is becoming 0. and the patient gets up...

makes sense ?

Answer 6

yeah! that does. thanks a lot :)

Answer 7

one more question. would the answers need units?

Answer 8

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...

Answer 9

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

Answer 10

haha, yes. that makes sense. thanks again.