# The percentage error in the Radioactive substance Population

• curious_mind
In summary: I felt I already showed my work and even posted original question in the thread. But elaborating more..We are given percentage error in half life measurement of radioactive substance as 10%. It is given as underestimated, which means the actual half-life should be more, ok?Now percentage error of any physical quantity is given by (Actual-Estimated)/Actual * 100% which is given 10%So (Actual-2.25)/Actual * 100% =10%This way I obtained actual half-life to be = 2.5 days.Now it is asked to find the percentage error in population of substance after 9 days.Which I am unable
curious_mind
Homework Statement
Initially the half-life is measured 2.25 days, but later it was found underestimated by 10%. It is required to find the percentage error in "Population" of the substance after 9 days.
Relevant Equations
## N = N_0 e^{-\lambda t} ##
Please check the question below as given originally. Answer given is 25%. I am unable to proceed.

It is given that the half-life is underestimated by 10% therefore it must be larger than originally estimated.
What I can find using the percentage error formula is ##\left( \dfrac{Actual-Estimated}{Actual} \right) \times 100% = \left( \dfrac{Actual-2.25}{Actual} \right) \times 100%=10%##

So, ##Actual = 2.5 ~days##
Now, I am unable to make relation of this with the population after 9 days, which is required to find in the question. The answer given is ##25%##. How it is obtained?

Thanks.

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What answer did you get, and how did you get there ?

hmmm27 said:
What answer did you get, and how did you get there ?
I am not getting required answer that's why posted question here. For The original question, I attached a picture. Answer given is 25%.

What I obtained is the actual half-life given the estimated half life and the underestimation percentage error of measuring half life.

It is Required to find the percentage error in the population ##N## after 9 days. I am unable to proceed for it.

curious_mind said:
I am not getting required answer that's why posted question here. For The original question, I attached a picture. Answer given is 25%.

What I obtained is the actual half-life given the estimated half life and the underestimation percentage error of measuring half life.

It is Required to find the percentage error in the population ##N## after 9 days. I am unable to proceed for it.
As @hmmm27 already said, please show your work. That you obtained a result that doesn't match a known answer is insufficient information for us to figure out what you did wrong, if anything.

kuruman said:
As @hmmm27 already said, please show your work. That you obtained a result that doesn't match a known answer is insufficient information for us to figure out what you did wrong, if anything.
I felt I already showed my work and even posted original question in the thread. But elaborating more..

We are given percentage error in half life measurement of radioactive substance as 10%. It is given as underestimated, which means the actual half-life should be more, ok?

Now percentage error of any physical quantity is given by (Actual-Estimated)/Actual * 100% which is given 10%

So (Actual-2.25)/Actual * 100% =10%

This way I obtained actual half-life to be = 2.5 days.

Now it is asked to find the percentage error in population of substance after 9 days.

Which I am unable to tell what to do next

You need to find the population with the correct half-life after 9 days. How will you do that? You have posted a "relevant equation." Do you think it could be a useful equation?

## 1. What is the percentage error in the Radioactive substance Population?

The percentage error in the Radioactive substance Population is a measure of how accurate the estimated population is compared to the actual population. It is calculated by taking the difference between the estimated population and the actual population, dividing it by the actual population, and multiplying by 100 to get a percentage.

## 2. How is the percentage error in the Radioactive substance Population calculated?

The percentage error in the Radioactive substance Population is calculated by taking the difference between the estimated population and the actual population, dividing it by the actual population, and multiplying by 100 to get a percentage. The formula is: (Estimated Population - Actual Population) / Actual Population * 100%

## 3. What factors can contribute to the percentage error in the Radioactive substance Population?

There are several factors that can contribute to the percentage error in the Radioactive substance Population. These include measurement error, sampling error, and human error in data collection or analysis. Other factors such as changes in the environment or population dynamics can also impact the accuracy of the estimated population.

## 4. How can the percentage error in the Radioactive substance Population be minimized?

To minimize the percentage error in the Radioactive substance Population, it is important to use accurate and precise measurement techniques, ensure a representative sample is collected, and carefully analyze the data. It is also important to consider any potential sources of error and try to control for them in the study design. Additionally, repeating the study multiple times and taking the average of the results can help reduce the overall error.

## 5. Why is it important to calculate the percentage error in the Radioactive substance Population?

Calculating the percentage error in the Radioactive substance Population is important because it allows scientists to assess the accuracy of their data and results. It also helps to identify any potential sources of error in the study, which can inform future research and improve the overall accuracy of population estimates. Additionally, understanding the percentage error can help to determine the reliability and validity of the study's findings.

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