Question

the half-life of a radioactive element X is 7 years.if 10g of X is released into an environment, find the age in which 10% of the radioactive nuclei are still present.

Answer 1

Hmm I'm not really familiar with half-life...
I'm thinking of it like this I guess:\[\Large\bf\sf x(0)=10g\]10 grams is our amount at time t=0.\[\Large\bf\sf x(7)=5g\]Cut in half after 7 years,\[\Large\bf\sf x(14)=2.5g\]\[\Large\bf\sf x(21)=1.25g\]Cut in half every 7 years.
So this looks like powers of 2, in multiples of 7.

I'm thinking it's something like this,\[\Large\bf\sf x(t)=10 \left(\frac{1}{2}\right)^{7t}\]

Answer 2

Is there a method for solving this type of problem?
I'm clearly missing the process here :(
Just kind of guessing right now.

Answer 3

that looks very much like my notes! thanks a bunch!

Answer 4

Cool! c:
Understand how to solve it?
Looks like you just need to know when x(t) = 1 or something.

Answer 5

im not sure if your answer is correct though but it helps!