Question

Question #2ac56

Answer 1

I think the answer is 7.2 secons.

An exponential decay function can be easily written as

`N(t) = N_0(t) *(1/2)^(t/t_(1/2))` , where

`N(t)` - the quantity that remains and has not yet decayed after a time t;
`N_0(t)` - the initial quantity of the substance that will decay;
`t_(1/2)` - the half-life of the decaying quantity;

We have `N(t) = 12.5` grams, and `N_0(t) = 100` grams, therefore

`12.5 = 100 *(1/2)^(t/t_(1/2))` ; we also know that the requested decay process took 21.6 seconds, so `t = 21.6` seconds.

`12.5/100 = (1/2)^(21.6/t_(1/2))`

`21.6/t_(1/2) = log_(1/2)(0.125)`

`21.6/t_(1/2) = 3`, which gives us `t_(1/2) = 7.2` seconds.