# Linearization of Inverse Proportionality

• max0005
In summary, the conversation discusses a problem with plotting data on a scatter diagram that shows an inverse proportionality between two sets of data. The speaker is seeking help to linearize the graph in order to estimate the half-life of the foam. Suggestions are made, including trying the log of the function, but the speaker is unsure of how to proceed. The potential for measurement error is also brought up.
max0005

## Homework Statement

Dear All,

I currently have a set of data which, when plotted on a scatter diagram, proves an inverse proportionality between two sets of data. (Please see attachment.)

I now need to linearize the graph as to estimate the half-life of the foam.

-

## The Attempt at a Solution

I tried to transform all y-values (y) into their corresponding 1/y values, thinking that inverting an inverse proportionality should have yielded a linear one, but it didn't help... Suggestions?

#### Attachments

• foam.jpg
17.9 KB · Views: 440
Have you tried the log of the function yet?

I get this..

#### Attachments

• foam.jpg
15.1 KB · Views: 399
Hmm... May I see the data sets?

It is only the last few points, beyond 20s, that deviate from a fairly good straight line and these points are probably the ones with greatest uncertainty...when the height of the foam is less than 0.5cm (5mm)...could you actually make these measurements to better than 1mm?

## 1. What is linearization of inverse proportionality?

Linearization of inverse proportionality is a mathematical technique used to transform a non-linear relationship between two variables into a linear relationship. This is done by manipulating the original equation in a way that one of the variables is now directly proportional to the other, making it easier to analyze and interpret the data.

## 2. Why is linearization of inverse proportionality important?

Linearization of inverse proportionality is important because it allows us to easily visualize and understand the relationship between two variables. It also makes it easier to perform calculations and make predictions based on the data. In addition, linear relationships are typically easier to model and analyze using mathematical and statistical techniques.

## 3. What is the difference between direct and inverse proportionality?

Direct proportionality is when two variables change in the same direction, meaning that when one variable increases, the other variable also increases. Inverse proportionality is when two variables change in opposite directions, meaning that when one variable increases, the other variable decreases.

## 4. How do you linearize a non-linear inverse proportionality equation?

To linearize a non-linear inverse proportionality equation, we can use the reciprocal of one of the variables. This means taking the inverse of the original equation, which will result in a linear relationship between the two variables. We can then plot the data on a graph and use linear regression to find the equation of the line.

## 5. In what real-world scenarios is linearization of inverse proportionality useful?

Linearization of inverse proportionality is useful in many real-world scenarios, such as when analyzing the relationship between the amount of gas used and the distance traveled by a car, or the relationship between the amount of fertilizer used and the crop yield in agriculture. It can also be used in physics to study the relationship between force and acceleration, or in economics to analyze the relationship between price and demand.

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