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?

Question

anonymous · Answer

@amistre64 can u help me?

amistre64 · Answer

i can

amistre64 · Answer

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

amistre64 · Answer

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
$$\frac{ln(1/2)}{14}=r$$

amistre64 · Answer

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

amistre64 · Answer

.125 = e^rt

ln(.125) = rt

ln(.125)
------- = t
    r

anonymous · Answer

so its 42