Question

a radioactive substance has a half-life of 20 days. how much time is required so that only 1/32 of the original amount remains?. find the rate of decay at this time

Answer 1

you must remember ..cuz i don't lol

but determine the constant with half life formula

then put the values int logn'/n formula

hope it helps

Answer 2

oh heck no

Answer 3

is something wrong ?

Answer 4

\[32=2^5\] so answer is 5 half lives

Answer 5

5 times 20 is 100 done

Answer 6

Decay rate is found by using the function A(t)=Pe^rt
Half of the substance remains after 20 days (50%=0.5 and 100%=1)
0.5=1e^20r, solve by using the natural log. ln (0.5)/20=r

That will give you the decay rate.
Then use that to find t (time at 1/32, so:
1/32=1e^(rate)t

I don't have a graphing calculator handy so I can't do the math, but that is the process of solving it.

Answer 7

in 20 days have
\[\frac{1}{2}\]
40 days
\[\frac{1}{4}\]
60 days
\[\frac{1}{8}\]
etc. so in 100 days
\[\frac{1}{2^5}\] aka \[\frac{1}{32}\]

Answer 8

sorry i am still so confused with this question

Answer 9

i know the formula for half-life but i dont know how to solve it

Answer 10

Look at my first post, that has the steps to solve it, I just can't do the math because I don't have a calculator. Basically find ln (0.5), then divide that number by 20. The number you get is the rate.

Then use the rate to find how much time it takes for the substance to decay until only 1/32 of it is left. so using the decay rate equation, place 1/32 as A(t) and plug in the other values P (intial amount) is 1, e is the natural number, and r is the rate you got in the first part of the problem.

Then just plug in the numbers: 1/32=1e^(rate)t and that is the same as:

ln (1/32)=(rate)*t
t=ln (1/32) / rate

And that value is the time in days it takes for the substance to decay to 1/32 of the original amount. Hope that helps!

Answer 11

probably too late for this to do any good, but the point is
\[(\frac{1}{2})^5=\frac{1}{32}\] meaning that it takes five half lives to get to
\[\frac{1}{32}\] you do not need e to the anything. one half life is 20 days. 5 half lives is 5 times 20 = 100 days. finish