Maths prob, help plz

More info please
I think you don't have the problem stated correctly. Either that your you don't have enough information. Normally it goes something like this:

"X percent of the molecules decay away every second. How long until half of the total is gone?"

Is that what you are looking for? Knowing how many decay is useless without knowing the entire count of molecules. Solving the above type of problem does involve logs though, so maybe you are looking for something else.

The hint that is given relates to a recurrence relation form and 'S' is to be the original number of molecules.

Ahh
Ok, now we can solve this.

At time zero, you have S molecules.
At time one sec, you have S*(1-x) molecules since S*x have decayed away.
At time two sec, you have S*(1-x)*(1-x) molecules. You see the pattern emerging here.

At time t, you have S*(1-x)^t molecules left.

What you want to know is when (1-x)^t = 1/2. I leave the rest for you to solve with the hint that you need to use logs.

ah ok thanks! I'm not veri good with working with logarithms but is this the correct approach?

(1-x)^t = 1/2

so taking the logs of both sides:

---> ln (1-x)^t = ln (1/2)
---> t ln (1) - t ln (x) = ln (1/2) [ or ln (0.5) ]


t ln (1/x) = ln (0.5)

solve for t:

t = ln (0.5)/ln (1/x)

sub for x = 0.000002

t = ln (0.5)/ln (1/0.000002)

Uh.....am I on the right track?

Not quite
Close, but you made one error.

ln(1-x) does not equal ln(1)-ln(x).

Starting at ---> ln (1-x)^t = ln (1/2)

---> t ln (1-x) = ln (1/2)
---> t = ln(1/2) / ln(1-x)

Plug in for x and solve.

ah thanks! got it now