Pressure and Volume -- are the growth/decay rates exponential?

Click For Summary
SUMMARY

The discussion centers on the analysis of growth and decay rates in the context of pressure and volume, specifically examining the equations P = 3.2c^-1.4 and f(v) = -8v^-0.4. The user explores whether these functions exhibit exponential decay, noting that both functions decrease in value but at varying rates. The first set of limits crosses the x-axis, indicating a decay that does not stabilize, while the second set remains above the x-axis, suggesting a different decay behavior. The conclusion drawn is that both functions represent forms of exponential decay, albeit with distinct characteristics.

PREREQUISITES
  • Understanding of exponential functions and their properties
  • Familiarity with calculus concepts, particularly integration
  • Knowledge of pressure-volume relationships in physics
  • Ability to analyze and interpret mathematical graphs
NEXT STEPS
  • Study the characteristics of exponential decay functions in detail
  • Learn about pressure-volume work in thermodynamics
  • Explore graphing techniques for visualizing decay rates
  • Investigate the implications of limits in calculus on function behavior
USEFUL FOR

Students in physics or mathematics, particularly those studying thermodynamics or calculus, as well as educators seeking to clarify concepts of exponential growth and decay.

lee123456789
Messages
90
Reaction score
5

Homework Statement



forumlate if its growth/decay is exponential
I have equation that i intergrated and found Pressure over volume = work done of pressure
P = 3.2c^-1.4
f(v) = -8v^-0.4
i set limits of 10x10^-6 --> 100x10^-6
and
10x10^-6 --> 100x10^-6 but i increase both values by 20x10^-6 every time for this one

Homework Equations

The Attempt at a Solution



i know they both decay and decrease in value by ruffly a half each time. but they slow down in decay and there decay rates slow down.
i know a exponential function is something power of x

second limits sets it doesn't cross the x-axis it stays just above it each time
first limits sets cross the x-axis and slows down but keeps on decreasing . it doesn't stay above a certain value. it keeps on decreasing

slightly confused
are these decay and is the function overall both examples exponential and exponential decay ?
 
Last edited by a moderator:
Physics news on Phys.org
Hello 1through9,
lee123456789 said:
forumlate if its growth/decay is exponential
I have equation that i intergrated and found Pressure over volume = work done of pressure
P = 3.2c^-1.4
f(v) = -8v^-0.4
This is not a problem statement. This way, helping becomes impossible !
 
  • Like
Likes   Reactions: Chestermiller and Phylosopher
Please write down the question. I cannot even guess why there is exponential decay to begin with.
 
forumulate if the decay/growth is exponential that is al lthe question has given

im just bit confused of expnential
i worked out and draw both grapth. one goes negative and one stays positive and just continuous hovers above the 0 mark of x axis. they both produce a curve. but one. but one of them continously decrease in valuve and never levels off
are these decay and is the function overall both examples exponential and exponential decay ?
 
lee123456789 said:
forumulate if the decay/growth is exponential that is al lthe question has given
Can't believe that. Is it about Little Red Riding Hood or is it about something else ? What ? Any context ?
 

Similar threads

  • · Replies 4 ·
Replies
4
Views
4K
Replies
3
Views
16K
Replies
13
Views
4K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 4 ·
Replies
4
Views
23K
Replies
3
Views
3K
  • · Replies 4 ·
Replies
4
Views
4K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 6 ·
Replies
6
Views
3K