You are here:

Calculus/a optimization problem

Advertisement

Expert: Alon Mandes - 10/16/2008


Question
1) According to the South Coast Air Quality Management District, the level of nitrogen dioxide, a brown gas that impairs breathing, present in the atmosphere on a certain may day in downtown Los Angeles is approximated by the model A(t)=t^3(t-7)^4+2018. 0 is less or equal to  t and t is less or equal to 7 where A(t) is measured in pollutant standard index (PSI) and t is measured in hours, with t=0 corresponding to 7 a.m.  At what time of day is the air pollution increasing and at what time of the day is the air pollution decreasing?

Answer
Ok, our target function is A(t)=t^3(t-7)^4+2018 . Let's derive it &
set the derivative equal to zero. We will follow the deriving rule:
(fg)'=f'g+fg' :
A'(t)=3t^2(t-7)^4+4t^3(t-7)^3
A'(t)=t^2(t-7)^3[3(t-7)+4t]
A'(t)=t^2(t-7)^3[7t-21]
A'(t)=0 -> t^2(t-7)^3[7t-21]
1st point of extrimum t^2=0 -> t=0      "which means 7:00 a.m "
2nd point of extrimum (t-7)^3=0 -> t=7  "which means 14:00 p.m "
3rd point of extrimum (7t-21)=0 -> t=3  "which means 10:00 a.m "
So, The pollution is decreasing between 10:00 - 14:00 .
& the pollution is increasing between 7:00 - 10:00 & after 14:00.

Alon.  

Calculus

All Answers

Answers by Expert:

Ask Experts

Volunteer

Alon Mandes

Expertise

Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .

Experience

1. I'm a team member of mathnerds (math site for answering questions) 2. I'm a team member in the Student's Union of the Technion, helping students who have problems in mathematics. 3. 2 years of experience as a math teacher in college. 4. I give free homework help for high school students in Mathematics & Physics. 5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" , "Complex Functions".

Organizations
Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.

Education/Credentials
M.A in Mathematics & Bs.c in Electronics.

©2012 About.com, a part of The New York Times Company. All rights reserved.