Question

How long, in years, will it take 80 kg of plutonium (half life 24 000 years) to decay to approximately 1.8 kg?

Answer 1

solve
\[1.8=80\times (\frac{1}{2})^{\frac{t}{24,000}}\] for \(t\)

Answer 2

first divide both sides by 80 to get
\[.0225=(\frac{1}{2})^{\frac{t}{24,000}}\] then change of base gives
\[\frac{t}{24,000}=\frac{\ln(.0225)}{\ln(.5)}\] and multiply by 24,000 and use a calculator

Answer 3

okay and can u see if i have the right answer for this?

Answer 4

i got 228 years

Answer 5

no that cannot be right

Answer 6

if the half life is 24,000 years then that is the time it will take to go from 80 to 40

Answer 7

oh sorry this answer is for a different questionj and i wanted u to check if i got the answer right

Answer 8

looks like about 131317
http://www.wolframalpha.com/input/?i=24000*ln%28.0225%29%2Fln%28.5%29

Answer 9

260 grams of a radioactive substance decays to 160 grams after 160 years. To the nearest year, what is the half-life of the substance?

Answer 10

is the answer for this 228

Answer 11

\[160=260(\frac{1}{2})^t\]
\[\frac{8}{13}=(\frac{1}{2})^t\]
\[t=\frac{\ln(\frac{8}{13})}{\ln(.5)}\]

Answer 12

sorry if im asking too many questions. can u help me out with a few more if you dont mind?

Answer 13

damn i made a mistake. have to multiply my answer by 160

Answer 14

i get 112

Answer 15

so what ever you get for t you multiply it by 160?

Answer 16

r u sure?

Answer 17

equation at the beginning should have been
\[160=260\times (\frac{1}{2})^{\frac{t}{160}}\]

Answer 18

can u help me with this one? A stock that Jane bought at $75 a share is now worth $629.86 a share. If it was averaged a 12% increase in value a year, then how many years has Jane owned the stock? Round off your answer to one decimal place.

Answer 19

solution method is identical, but you should end up with
\[\frac{t}{160}=\frac{\ln(\frac{8}{13})}{\ln(.5)}\]
\[t=160\times \frac{\ln(\frac{8}{13})}{\ln(.5)}\]\]

Answer 20

\[629.86=75(1.12)^t\] solve for t

Answer 21

so would it be ln629.86/ ln 75

Answer 22

?