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# Exponential Functions... watch

1. Hi. I've been looking at this since yesterday and I just cannot solve it (My basic algebra has gone out of the window coz I've not been so much out of practise, but I didn't really work on maths last year and now paying for it )

But anyway could someone help me with this please?

Radioactive mass, Mg is given my M=25e^-0.0012t, where t = time (secs) from 1st obvservation.

What is the half life?

Thanks

For mathematicians who have never studied chemistry

A half life is the time it takes for a radioactive mass to decay to half of its mass
2. you know that at t=0, the mass is 25, so if you put M=25/2 you can solve for t to find the half life
3. (Original post by sonofdot)
you know that at t=0, the mass is 25, so if you put M=25/2 you can solve for t to find the half life
Its the solving I'm having the problem with

using 12.5 for M is about as far as I got (plus variations of taking e across as ln)
4. (Original post by Loz17)
Its the solving I'm having the problem with

using 12.5 for M is about as far as I got (plus variations of taking e across as ln)
Well it sounds like you're on the right lines - if you post your working it may be easier to see where you're getting stuck
5. (Original post by sonofdot)
Well it sounds like you're on the right lines - if you post your working it may be easier to see where you're getting stuck
12.5=25e^-0.0012t

12.5ln(-0.0012t) = 25

I dunno if I did that right

Its been almost a year since I did this last and I never really practised it then
6. (Original post by Loz17)
12.5=25e^-0.0012t

12.5ln(-0.0012t) = 25

I dunno if I did that right

Its been almost a year since I did this last and I never really practised it then
That's not quite right. Remember that ln is the inverse of the exponential function, so . The easiest way to get this to work is to get e^stuff on its own on one side of the equation, so divide through by 25 to get 0.5 = e^(-0.0012t) and then try taking logs of both sides
7. Ahh yea

But ln(-something) is impossible isn't it?
8. (Original post by Loz17)
Ahh yea

But ln(-something) is impossible isn't it?
you have got ln here only -something read sonfodot's post
9. (Original post by rbnphlp)
you have got ln here only -something read sonfodot's post
I mean

Once I have ln(0.5) = ln(-0.0012)t

How do I get ln(-0.0012)? It says math error on calculator

Sorry, I'm not the best at maths at all
10. (Original post by Loz17)
I mean

Once I have ln(0.5) = ln(-0.0012)t

How do I get ln(-0.0012)? It says math error on calculator

Sorry, I'm not the best at maths at all
not quite. you get . Since all of the -0.0012t is the power of e, when you log it you just get -0.0012t on that side
11. (Original post by Loz17)
I mean

Once I have ln(0.5) = ln(-0.0012)t

How do I get ln(-0.0012)? It says math error on calculator

Sorry, I'm not the best at maths at all
Thats where the error is
As sonfodots post says when you take ln(e^something) you only get something not ln(something)...

so here you would have

12. Do you see how you go from e to ln?
13. (Original post by rbnphlp)
Thats where the error is
As sonfodots post says when you take ln(e^something) you only get something not ln(something)...

so here you would have
Ahhh ok I get it now

Thank you both

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