- #1

curious_mind

- 21

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- 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.

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.