Related Rate Problem: Finding the Rate of Concentration Decrease at Time t

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SUMMARY

The discussion focuses on solving a related rates problem involving the concentration of H3O in a solution with a pH of 3. The pH changes at a rate of 0.01 per unit time, and the concentration of H3O is defined by the equation [H3O] = 10^-pH. By applying the chain rule, participants are guided to express the rate of change of concentration in terms of the rate of change of pH. This approach simplifies the calculation of the rate at which the concentration of H3O is decreasing at time t.

PREREQUISITES
  • Understanding of related rates in calculus
  • Familiarity with the chain rule in differentiation
  • Knowledge of pH and its relationship to H3O concentration
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study the chain rule in calculus for related rates problems
  • Learn about the relationship between pH and hydrogen ion concentration
  • Practice solving related rates problems with different functions
  • Explore applications of related rates in real-world scenarios
USEFUL FOR

Students in calculus courses, particularly those studying related rates, and anyone needing to understand the relationship between pH and concentration in chemical solutions.

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Related Rate Problem...HeLp!

Homework Statement


The ph of a solution is 3, ph changes at a rate of 0.01 at time t and the concentration of H3O is 10^-ph. At what rate is concentration decreasing at time t.


Homework Equations





The Attempt at a Solution


I need someone to walk me through this if possible..I've never done a related rate question (or if I did I don't remember).
 
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BuBbLeS01 said:

Homework Statement


The ph of a solution is 3, ph changes at a rate of 0.01 at time t and the concentration of H3O is 10^-ph. At what rate is concentration decreasing at time t.


Homework Equations





The Attempt at a Solution


I need someone to walk me through this if possible..I've never done a related rate question (or if I did I don't remember).

First things first.

Let's say you have a function y(x) and x itself is a function of time x(t). So we have y(x(t)).

If you are given dx/dt, can you write down the expression for dy/dt in terms of dx/dt? (it's basically the chain rule). If you know this, the rest will be straightforward.
 
Last edited:

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