Question #1f8ff
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"Find the sum of the integers between 2 and 100 which are divisible by 3 ?"
We can use a radioactive decay equation.
Radioactive decay is a random process, so we cannot exactly know which atom or the order that the atoms are going to decay. But, a formula can work to find the general half-life of a substance.
It is given by
#N(t)=N_0(1/2)^(t/(t_1/2))#
#N(t)# is the final amount of substance
#N_0# is the original amount of the substance
#t# is the time
#t_(1/2)# is the half-life of the substance
So, we can derive the half-life of the substance by rearranging the equation. Our original equation is
#N(t)=N_0(1/2)^(t/(t_1/2))#
Dividing by #N_0# gives us
#(N(t))/N_0=(1/2)^(t/(t_1/2))#
Using the logarithm properties, we get that
#t/(t_(1/2))=log_(1/2)((N(t))/N_0)#, and then we can inverse and get the reciprocal, which is
#(t_(1/2))/t=1/log_(1/2)((N(t))/N_0)#
Solving for #t_(1/2)#, we get
#t_(1/2)=t/log_(1/2)((N(t))/N_0)#
