# Rate of change, derivatives problem .

• manik
In summary, the conversation is about calculating the rate of change for the percentage of Canadians between 15 and 19 who smoke. The table provided shows the percentage for males and females over a period of 10 years. The suggested method is to approximate linearly between two points and use that as an approximation for the rate of change. The final rate of change can be calculated by subtracting the percentage from one year to the next. It is important to note that the table shows the percentage and not the actual rate of change.
manik
rate of change, derivatives problem...

This table shows the rate of change Canadians who are between 15 and 19 and who smoke...

http://img155.imageshack.us/img155/8915/asdce2.jpg

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if you want people to help, you are going to have to show what you have tried so far... have you tried graphing the data and using linear approximations?

i tried graphing it on a TI-84, and found the regression and its a cubic equation i think..

i mean if someone can possibly get me started or something i would appreciate it as i am unsure how to find the rate of change for male and female

with a table of data, the best you are going to do without using regression is to approximate linearly between any two points and use that as an approximation to the rate of change in that two year period. Doing that, you can answer the two questions given to you.

can u do 1 for me (like male) just to see what you mean.. then i should be able to do the female..

First, state your problem correctly! That table is obviously not the "rate of change of Canadians who are between 15 and 19 and who smoke" it is the percentage of such Canadians who smoke. You need to calculate the rate of change yourself. Since the change in time is just one year you need only subtract each years percentage from the next years percentage. In what year do you get the same answer for both males and females? Is the final rate of change positive or negative?

## 1. What is the rate of change?

The rate of change is the speed at which a variable is changing over time. It is calculated by dividing the change in the variable by the change in time.

## 2. What is a derivative?

A derivative is a mathematical concept that represents the rate of change of a function at a specific point. It is the slope of a tangent line at that point on the function's curve.

## 3. How do you find the derivative of a function?

To find the derivative of a function, you can use the derivative rules such as the power rule, product rule, quotient rule, and chain rule. These rules allow you to find the derivative of a function with respect to its independent variable.

## 4. What are derivatives used for?

Derivatives are used in various fields of science and mathematics, including physics, economics, and engineering. They are used to calculate rates of change, determine maximum and minimum values, and solve optimization problems.

## 5. How can I improve my understanding of derivatives and rate of change?

To improve your understanding of derivatives and rate of change, it is important to practice solving problems and to seek help from teachers or tutors if needed. You can also read textbooks or watch online tutorials to deepen your knowledge on the subject.

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