soccergal12 3 years 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.

1. ganeshie8

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

2. soccergal12

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

3. ganeshie8

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)

4. soccergal12

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?

5. ganeshie8

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

6. soccergal12

yeah! that does. thanks a lot :)

7. soccergal12

one more question. would the answers need units?

8. ganeshie8

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...

9. ganeshie8

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

10. soccergal12

haha, yes. that makes sense. thanks again.