Question

Calculus help: (Question in reply section)
Codeine phosphate is a drug used as a painkiller. A common brand contains 30 mg of codeine. Samples of blood were taken at regular time intervals from a patient who had taken a pill containing 30 mg of codeine. The amount of codeine in the bloodstream was determined every 30 min for 3 h. The data are shown in the table below.
Time After Consumption (min): 30, 60, 90, 120, 150, 180
Amount of Codeine in Blood (mg): 27.0, 23.5, 21.2, 18.7, 16.6, 14.5

Answer 1

I have dont part A but I dont know how to do part b. I am not to use a graphing calculator

a) Create a scatter plot of the data and determine a suitable equation to model the amount of codeine in the bloodstream t min after taking the pill. Justify your choice of models.

b) Use the model to determine the instantaneous rate of change in the amount of codeine at each time given in the chart. How does it relate to the amount of codeine in the blood?

Answer 2

If you have the model equation, you can take the derivative, then plug in each time into the derivative.

Answer 3

Ok so I think the model equation is A=31.0213e^-0.00463t. Would the derivative be -0.1436te^-1.00463? Then I would just sub in the different times into t? For example I subbed in the first time and got -1.57750 as my answer

Answer 4

I get -0.1436e^-0.00463t as the derivative.

Answer 5

You don't subtract 1 from the exponent in an exponential derivative. Only when it is a variable raised to a number.

Answer 6

Ohh ok thank! I subbed in 30 into t and got -0.124498.
So when I repeat this with the rest of the times, do I just compare the answers to see how they relate to the amount of codeine in blood?

Answer 7

Yup! See how they relate to the rate of change of codeine in the blood.

Answer 8

Ok thanks a lot for your help!

Answer 9

No worries :)