# Maclaurin Series - Exponentials 2 (Isaac Physics)

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Part C (i). I have that ΔE = E(T+t) - E(t), and as E(T+t) =E(t)e^(-γt) , then ΔE = E(t)((e^(-γt)-1). I'm pretty sure the fraction I'm looking for is ΔE/E(t), which would equal e^(-γt)-1 , however this is wrong. Can someone help me with this part of the question please?

Part C (i). I have that ΔE = E(T+t) - E(t), and as E(T+t) =E(t)e^(-γt) , then ΔE = E(t)((e^(-γt)-1). I'm pretty sure the fraction I'm looking for is ΔE/E(t), which would equal e^(-γt)-1 , however this is wrong. Can someone help me with this part of the question please?

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(Original post by

https://isaacphysics.org/questions/m...5-6c2b8159b501

Part C (i). I have that ΔE = E(T+t) - E(t), and as E(T+t) =E(t)e^(-γt) , then ΔE = E(t)((e^(-γt)-1). I'm pretty sure the fraction I'm looking for is ΔE/E(t), which would equal e^(-γt)-1 , however this is wrong. Can someone help me with this part of the question please?

**domm1**)https://isaacphysics.org/questions/m...5-6c2b8159b501

Part C (i). I have that ΔE = E(T+t) - E(t), and as E(T+t) =E(t)e^(-γt) , then ΔE = E(t)((e^(-γt)-1). I'm pretty sure the fraction I'm looking for is ΔE/E(t), which would equal e^(-γt)-1 , however this is wrong. Can someone help me with this part of the question please?

No idea why they want it that way, but it works.

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Oh yes now I've got it, weird they wanted it that way though, I thought that generally when you're thinking of a change in something you'd take the initial value from the final (even though the vice versa works perfectly fine), but I guess it's maybe because e^(-γt) is a value <1, so by finding the change by subtracting final from initial we get a positive value for the fractional change in energy which is a bit nicer than a negative? My only thought for why they'd want it that way instead.

**domm1**)Oh yes now I've got it, weird they wanted it that way though, I thought that generally when you're thinking of a change in something you'd take the initial value from the final (even though the vice versa works perfectly fine), but I guess it's maybe because e^(-γt) is a value <1, so by finding the change by subtracting final from initial we get a positive value for the fractional change in energy which is a bit nicer than a negative? My only thought for why they'd want it that way instead.

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Could be that since they are talking about decay, then it's implicit in the question that they want the fractional loss, hence....

**ghostwalker**)Could be that since they are talking about decay, then it's implicit in the question that they want the fractional loss, hence....

I found the Maclaurin series for e^(-γt) which gave '1 - γt + (γ^2(t)^2)/2 ', and so I substituted this into the equation for the fractional loss, 1-e^(-γt), and got an answer of 'γt - (γ^2(t)^2)/2 ', but is incorrect?

Last edited by domm1; 1 week ago

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I've done Part B, however I am quite lost how I have not got the correct answer.

I found the Maclaurin series for e^(-γt) which gave '1 - γt + (γ^2(t)^2)/2 ', and so I substituted this into the equation for the fractional loss, 1-e^(-γt), and got an answer of 'γt - (γ^2(t)^2)/2 ', but is incorrect?

**domm1**)I've done Part B, however I am quite lost how I have not got the correct answer.

I found the Maclaurin series for e^(-γt) which gave '1 - γt + (γ^2(t)^2)/2 ', and so I substituted this into the equation for the fractional loss, 1-e^(-γt), and got an answer of 'γt - (γ^2(t)^2)/2 ', but is incorrect?

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*must*be an energy change within the system, or do we not?).

Last edited by domm1; 1 week ago

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Oh okay I understand, however how comes you still consider the T^1 term? I understand that the T^2 term would be a lot smaller in comparison, but is this the reason for the remaining of the T^1 term? Is it also for the fact that by ignoring the T^1 term as well, you get the approximation for the fractional change equal to zero, which would be less accurate than just considering the T^1 term (as we also know there

**domm1**)Oh okay I understand, however how comes you still consider the T^1 term? I understand that the T^2 term would be a lot smaller in comparison, but is this the reason for the remaining of the T^1 term? Is it also for the fact that by ignoring the T^1 term as well, you get the approximation for the fractional change equal to zero, which would be less accurate than just considering the T^1 term (as we also know there

*must*be an energy change within the system, or do we not?).If you're interested in what the change is, then dropping the T^1 term and saying it's 0, would be a 100% error relative to the true value. As an approximation, it leaves a great deal to be desired

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