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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: clarke54321 on July 09, 2016, 12:26:19 pm

Title: Unit 1/2 Question
Post by: clarke54321 on July 09, 2016, 12:26:19 pm: Hi everyone,

Could I please have some help with this half-life question?

The mass M of a radioactive substance is initially 10 g and 40 years later its mass is 9.2 g. Calculate its half-life.

Thank-you :)
Title: Re: Unit 1/2 Question
Post by: qazser on July 09, 2016, 12:52:15 pm: Fixing TeX

$N_{o}e^{-kt}$

$N_{o}$ is the initial value of the substance. Hence let it be 10 and let t be 0(Initial value).

$10e^{-k0}=10$

In 40 years, the equation will look like this

$10e^{-k \times 40}=9.2$

Hence solve for k

$\mbox{k=0.0020}$

Now, we know that half life of a substance is the time taken for it mass to be halved. Therefore, let our equation=5

$\mbox{10e^{-0.0020t}=5}$

Solve for t

Hence t=332.51 years
Title: Re: Unit 1/2 Question
Post by: clarke54321 on July 09, 2016, 01:03:47 pm: Quote from: qazser on July 09, 2016, 12:52:15 pm
Fixing TeX

$ N_{o}e^{-kt} \mbox{So N_{o} is the initial value of the substance. Hence let it be 10 and let t be 0(Initial value).} 10e^{-k0}=10 \mbox{In 40 years, the equation will look like this} 10e^{-k\times 40}=9.2 \mbox{Hence solve for k} \mbox{\therefore k=0.0020 approximately} \mbox{the let 10e^{-0.0020\times t}=5} \mbox{Solve for t} \mbox{Hence t=332.51 years} $

I can't see your working
Title: Re: Unit 1/2 Question
Post by: qazser on July 09, 2016, 01:14:25 pm: Quote from: clarke54321 on July 09, 2016, 01:03:47 pm
I can't see your working

Check now. Sorry
Title: Re: Unit 1/2 Question
Post by: clarke54321 on July 09, 2016, 01:55:21 pm: Quote from: qazser on July 09, 2016, 01:14:25 pm
Check now. Sorry

Fantastic. Thanks Qazser! :)