Question

A certain radioactive substance has a half-life of 14 days. How many days will it take until there is only 12.5% of the original amount remaining?

Answer 1

@amistre64 can u help me?

Answer 2

i can

Answer 3

we need to determine the rate .... and that can be done generically with some algebra

Answer 4

spose we start with P and we end up with P/2 in a given amount of time

\[P/2=Pe^{rt}\]divide of the P
\[1/2=e^{rt}\]ln to undo the e
\[ln(1/2)=rt\]divide off the t to solve for r
\[\frac{ln(1/2)}{t}=r\]and since we know t is 14 days
\[\frac{ln(1/2)}{14}=r\]

Answer 5

now, spose we start with 100 parts and want to know when we will end up with 12.5 parts; we need to solve for t this time

\[12.5 = 100e^{rt}\]

work it thru and get to the end , plug in our r value we found to keep the clutter down

Answer 6

.125 = e^rt

ln(.125) = rt

ln(.125)
------- = t
r

Answer 7

so its 42