Expert: Paul Klarreich - 5/2/2008

Question
The eating behavior of a typical human during a meal can be described by
I(t)=27+ 72t - 1.5t^2
where t is the number of minutes since the meal beagn, and I(t) represents the amount (in grams) that the person has eaten at time t.
a)  Find the rate of change of the intake of food for the particular person 5 minutes into a meal and interpret.
b.  Verify that the rate in which food is consumed is zero 24 minutes after the meal starts.
c.  Comment on the assumptions and usefulness of this function after 24 minutes.  Given this fact, determine a logical range for this function.


Answer
Questioner:   Amber
Category:  Calculus
Private:  No
 
Subject:  derivatives
Question:  The eating behavior of a typical human during a meal can be described by
I(t)=27+ 72t - 1.5t^2
where t is the number of minutes since the meal beagn, and I(t) represents the amount (in grams) that the person has eaten at time t.
a)  Find the rate of change of the intake of food for the particular person 5 minutes into a meal and interpret.
b.  Verify that the rate in which food is consumed is zero 24 minutes after the meal starts.
c.  Comment on the assumptions and usefulness of this function after 24 minutes.  Given this fact, determine a logical range for this function.


If I(t) = amount eaten after t minutes, then
I'(t) = rate of eating at t minutes. (basic interpretation of any derivative.)

So I'(t) = 72 - 3t, and

I(5) = 72 - 15 = 57 grams/minute being eaten at t = 5.

I'(24) = 72 - 3(24) = 0, of course.

You can draw your own conclusions, now.  Mine would be:

At t = 24, you stop eating.  I suppose the function will be meaningless outside the [0,24] interval.