Question

after 100 days a particular radioactive substance decays to 30% of its original amount. find the number of days it will take for this substance to decay to 60% of its original amount

Answer 1

Are you given the original amount?

Answer 2

no. that's the question

Answer 3

I'm assuming the original amount is 100%

Answer 4

good assumption

Answer 5

30 = 100 e^(100r) solve for r

Answer 6

doesn't matter
sovle
\[(.3)^{\frac{t}{100}}=.6\] for t

Answer 7

or use amsitre method, find r, and then go back and solve for t
either way

Answer 8

\[\frac{t}{100}=\frac{\ln(.6)}{\ln(.3)}\]
\[t=\frac{100\ln(.6)}{\ln(.3)}\] then a calculator

Answer 9

thank you guys!

Answer 10

42.4

Answer 11

since u can't have 42.4 days you round it off to 42 days.

Answer 12

if i use amistre 64's method...how would i go back and solve for t?

Answer 13

Amistre's method:

\[0.3 = e^{100r} \rightarrow r = \frac {1}{100} \ln 0.3\]\[60 = 100e^{\frac {t}{100} \ln 0.3} \rightarrow 0.6 = e^{\frac {t}{100} \ln 0.3} \rightarrow t = \frac {100 \ln 0.6}{\ln 0.3} \approx 42.428 days\]

Answer 14

thank u

Answer 15

welcome =)