# The percentage error in the Radioactive substance Population

• curious_mind
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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Gold Member
What answer did you get, and how did you get there ?

curious_mind
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.

Homework Helper
Gold Member
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.

curious_mind
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