Math Is Fun Forum

Jennifer15

Member

Registered: 2008-04-09

Posts: 2

fractional exponents

exponential decay of radioactive material:

the half life of a radioactive material is 25 years
started with 200 mg of material
how many years will it take to be left with 25 mg

            t/n
M=C(½)

M = final mass
C = original mass
½ = decay factor
t = time
n = half life

How do you isolate the fractional exponent?
(this is a grade 9 math question - we are not familiar with logarithms yet - maybe I am making this too complicated.... )

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: fractional exponents

1/2 life = 1/2 = df
M = 25
C = 200

75 = 3*25 years is answer = n *  [ log (M/C) / log(df)]

The mass became 1/8th the size and is going by 1/2's in 25 years.
log(1/8) / log (1/2) = 3 half-life periods = 3 * 25 = 75 years.
also,
log(8) / log (2) = 3 too!!!  Because 1/1 = -1/-1    The reciprocals inside a log just goes negative for log answer.
Like log(55) = - log(1/55)
and log(100) = - log(1/100)

Sorry I just noticed you couldn't use logs.  Woops.
You could just guess answers till you come up with 3 years.
200 at 0 years
100 at 1*25 year
50 at 2*25 years
25 at 3*25 years.

And the 175 mg of material will be a combination of other elements, since
they decay in strange ways into other things.

Last edited by John E. Franklin (2008-04-09 09:19:45)

---

igloo myrtilles fourmis

Jennifer15

Member

Registered: 2008-04-09

Posts: 2

Re: fractional exponents

Thanks, yes, keeping it simple, I just used a chart until I got down to 25 in 75 years.
thanks again