Question

The half-life of thorium-229 is 7340 years. How long will it take for a sample of this substance to decay to 20% of its original amount?
A=Aoe^kt

Answer 1

set
\[\left(\frac{1}{2}\right)^\frac{t}{7340}=.2\] and solve for \(t\)

Answer 2

change of base formula gives
\[\frac{t}{7340}=\frac{\ln(.2)}{\ln(.5)}\] so
\[t=\frac{7340\ln(.2)}{\ln(.5)}\]

Answer 3

ok

Answer 4

you might notice i did not use
\[A=A_0e^{kt}\]
you can use that too but it takes longer, because first you have to find \(k\)
i only used the numbers that were given

Answer 5

so the answer is?

Answer 6

you need a calculator at this point, if you want a decimal

Answer 7

this is what i get
http://www.wolframalpha.com/input/?i=7340*ln%28.2%29%2Fln%28.5%29

Answer 8

that doesnt help

Answer 9

so i take .2/.5?
i got .4

Answer 10

thanks