Rate of decay question, need halp! (1 Viewer)

[Frostbitten]

Need help with this question, it is annoying me.

The rate of decay of a radioactive source is given by the formula dm/dt=-km
where k is a positive constant, m is the mass in grams, and t is the time in years.

i) If the initial mass of the source was a grams, find an equation for the mass m grams remaining after t years.


Thankyou, reps to a speedy reply!

 

[Frostbitten]

Beep bop bu ba beep bump

 

[Makematics]

Need help with this question, it is annoying me.

The rate of decay of a radioactive source is given by the formula dm/dt=-km
where k is a positive constant, m is the mass in grams, and t is the time in years.

i) If the initial mass of the source was a grams, find an equation for the mass m grams remaining after t years.


Thankyou, reps to a speedy reply!

 

[braintic]

Students are not required to derive this equation in Ext 1. It only needs to be written down.

 

[Frostbitten]

Hmm, in my booklet it takes a different route, I can't quite make much sense out of the initial step.

The answer starts out as follows:
dm/dt=-km
To find the mass remaining after t years, the equation must be integrated:

Step 1=> ∫(dm/m)=-k∫(dt)
Step 2=> ln m=-kt+c
Step 3=>m=e^(-kt+c)

How exactly did it go from step 1 to step 2? What is going on?

 

[Makematics]

Hmm, in my booklet it takes a different route, I can't quite make much sense out of the initial step.

The answer starts out as follows:
dm/dt=-km
To find the mass remaining after t years, the equation must be integrated:

Step 1=> ∫(dm/m)=-k∫(dt)
Step 2=> ln m=-kt+c
Step 3=>m=e^(-kt+c)

How exactly did it go from step 1 to step 2? What is going on?

what is hard to see? both sides are being integrated. LHS with respect to m, RHS with respect to t. And that isnt really a different route. it has just rearranged it for integration. the method the textbook used is more commonly used in higher levels maths, and as braintic said isnt required in 2u. that is why i wrote it as i did, because apparently it is easier to understand than separating it as the answer you posted has.

 

[Frostbitten]

what is hard to see? both sides are being integrated. LHS with respect to m, RHS with respect to t. And that isnt really a different route. it has just rearranged it for integration. the method the textbook used is more commonly used in higher levels maths, and as braintic said isnt required in 2u. that is why i wrote it as i did, because apparently it is easier to understand than separating it as the answer you posted has.

Was not thinking clearly, makes sense now. Thank you for your enlightenment. Repped.