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

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In summary, the problem involves finding the rate at which the concentration of H3O is decreasing at a given time, based on the changing pH and concentration. This can be solved using the chain rule.
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BuBbLeS01
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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.
 
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1. What are related rate problems?

Related rate problems involve finding the rate of change of one quantity with respect to another in a given situation. This type of problem is commonly used in mathematics and physics to model real-world situations.

2. How do I solve a related rate problem?

To solve a related rate problem, you need to identify the given quantities and the rate at which they are changing. Then, use the chain rule and other calculus techniques to set up an equation and solve for the desired rate of change.

3. What is the chain rule?

The chain rule is a formula used in calculus to find the derivative of a composite function. In related rate problems, it is used to find the rate of change of one quantity in terms of another.

4. What are some common applications of related rate problems?

Related rate problems are commonly used in physics to model motion, such as the rate at which a car is accelerating. They are also used in economics to analyze changes in production and sales, and in biology to study population growth.

5. How can I check my answer for a related rate problem?

To check your answer for a related rate problem, you can use the given quantities and your calculated rate of change to see if they are consistent with the situation described. You can also take the derivative of your final equation to see if it matches the given rate of change.

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