Pharmacy exam 2018-12-17
Degrees: Pharmacy and Biotechnology
Date: Dic 17, 2018
Question 1
A organism metabolizes alcohol at a rate half of the present amount per minute. If initially there is no alcohol and we start to introduce alcohol in the organism at a constant rate of 2 ml/min, how much alcohol will there be in the organism after 5 minutes?
Differential equation:
Solution:
Question 2
The amount
Question 3
A capsule has pyramidal shape with base a rectangle of sides
- How must change the dimensions of the capsule to increase the volumen the most? What would be the rate of change of the volume if we changed the dimensions in such a way?
- If we start to change the dimensions of the capsule such that the largest side of the rectangle decreases half of the increase of the smaller side, and the height increases the double of the increase of the smaller side, what will the rate of change of the volume be?
Remark: The volume of a pyramid is
and the volume will increase cm /s if we change the dimensions of the capsule following this direction.- Directional derivative of
in along the vector : cm /s.
Question 4
The yield of a crop