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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: tolga on February 09, 2010, 08:14:55 pm

Title: Help on Exponential and Logarithmic modelling
Post by: tolga on February 09, 2010, 08:14:55 pm: Five grams of a radioactive substance is decaying so that the amount, A grams, that is left after t days, is given by the formula A=5e^-kt.

a) Find the value of A when the number of grams of the radioactive substance has been halved.
b) Rearrange the equation so that the t is the subject of the equation.

Note:Can you please show full working out
Title: Re: Help on Exponential and Logarithmic modelling
Post by: the.watchman on February 09, 2010, 08:18:55 pm: a) $A=\frac{1}{2} \times 5 = \frac{5}{2}$

b) $A = 5e^{-kt}$

$\frac{A}{5} = e^{-kt}$

$-kt = log_e\frac{A}{5}$

$t = -\frac{1}{k}log_e\frac{A}{5}$
Title: Re: Help on Exponential and Logarithmic modelling
Post by: tolga on February 09, 2010, 08:29:50 pm: for part a what happened to e^-kt
Title: Re: Help on Exponential and Logarithmic modelling
Post by: the.watchman on February 09, 2010, 08:31:51 pm: Quote from: tolga on February 09, 2010, 08:29:50 pm
for part a what happened to e^-kt

It only asks for the value of A, which is the weight of what's left.
Therefore, A is half of the original amount (5 grams) and so is 5/2
Title: Re: Help on Exponential and Logarithmic modelling
Post by: superflya on February 09, 2010, 08:41:47 pm: lulz tolga dont make a question seem harder than it actually is :P some q's are very straightforward but are harder to pick up and people usually go wrong as they try and over-complicate things.
Title: Re: Help on Exponential and Logarithmic modelling
Post by: the.watchman on February 09, 2010, 08:42:44 pm: Quote from: superflya on February 09, 2010, 08:41:47 pm
lulz tolga dont make a question seem harder than it actually is :P some q's are very straightforward but are harder to pick up and people usually go wrong as they try and over-complicate things.

Lol, yeah superflya is right