
Calculus Calculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
May 29th, 2018, 08:08 PM  #1 
Newbie Joined: May 2018 From: Canada Posts: 2 Thanks: 0  Challenging Derivatives of Exponential and Sinusoidal Functions task question
A common brand contains 30 mg of codeine. Since it is physically addictive and has other unwanted side effects, it is important to avoid an overdose while helping to relieve pain symptoms such as those caused by a headache. 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 attached. 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? c) It is recommended that a second pill be taken when 90% of the codeine is eliminated from the body. When would this occur? d) Assume that the same model applies to the second pill as to the first. Suppose the patient took a second pill one hour after consuming the first pill. • Create a model for the amount of codeine in the patient’s bloodstream t min after taking the first pill. • Determine the maximum amount of codeine in the patient’s bloodstream. • Determine when 90% of the maximum amount would be eliminated from the body. e) If the patient were to delay taking the second pill, how would it affect the results from part d)? Table.jpg Last edited by skipjack; May 30th, 2018 at 12:04 AM. 
May 29th, 2018, 11:55 PM  #2 
Senior Member Joined: Aug 2012 Posts: 2,044 Thanks: 584 
I'd definitely use Zorn's lemma.

May 30th, 2018, 01:14 PM  #3 
Global Moderator Joined: May 2007 Posts: 6,612 Thanks: 617 
Try exponential first $30e^{kt}$.

May 31st, 2018, 04:18 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 19,713 Thanks: 1806 
That was my thinking as well. Curiously, $30.4e^{kt}$ provides a better fit to the given data.


Tags 
challenging, derivatives, exponential, functions, question, sinusoidal, task 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Derivatives of Exponential and Log Functions  atari  Calculus  3  February 20th, 2016 11:39 PM 
Derivatives, trignometric functions and exponential functions  Nij  Calculus  2  November 25th, 2015 06:20 AM 
derivatives of exponential functions  pomazebog  Calculus  2  March 5th, 2012 08:23 AM 
Derivatives of exponential and log functions review help!  ProJO  Calculus  4  March 6th, 2011 09:49 AM 