Determining the time at which concentration begins to decrease

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SUMMARY

The discussion centers on determining the precise time at which concentration begins to decrease in a given context. Participants clarify that the time of interest is not simply the fifth hour but rather the moment after five hours and 24 minutes. The key takeaway is that a function is increasing when its derivative is positive and decreasing when its derivative is negative, which is essential for accurately identifying the time of concentration decrease.

PREREQUISITES
  • Understanding of calculus, specifically derivatives
  • Familiarity with functions and their behavior
  • Knowledge of concentration-time relationships in scientific contexts
  • Ability to interpret mathematical wording and phrasing
NEXT STEPS
  • Study the concept of derivatives in calculus
  • Learn about increasing and decreasing functions
  • Explore real-world applications of concentration functions
  • Review examples of concentration decay in chemistry
USEFUL FOR

This discussion is beneficial for students in mathematics and chemistry, particularly those studying calculus and concentration dynamics. It is also useful for educators seeking to clarify concepts related to function behavior.

ttpp1124
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Homework Statement
The question asks, "at what time.." does that mean at the fifth hour? Or after five hours and 24 minutes? I'm stuck with wording my answer
Relevant Equations
n/a
IMG_4248.jpg
 
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ttpp1124 said:
Homework Statement:: The question asks, "at what time.." does that mean at the fifth hour? Or after five hours and 24 minutes? I'm stuck with wording my answer
Relevant Equations:: n/a

View attachment 262780
Your approach to determining the time when the concentration begins to decrease makes no sense to me. And the time for concentration to be equal to zero is at time t = 0 only. Please describe your rationale for determining the time when the concentration begins to decrease.
 
"At what time does the concentration begins (sic) to decrease?"
A function is increasing if its derivative is positive; a function is decreasing if its derivative is negative.
 

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