Question

A certain radioactive isotope has a half-life of approximately 900 years. How many years would be required for a given amount of this isotope to decay to 70% of that amount?

Answer 1

A=A0 e^rt

Answer 2

1/2 = e^r(900)

Answer 3

solve for r

Answer 4

can you continue and show work

Answer 5

\[e^{900r}=1/2\]
900 r ln e= ln 1/2
900 r= ln 1/2

Answer 6

i have an idea

Answer 7

write the formula as \[Q = Q_0(\frac{1}{2})^{\frac{t}{900}}\]

Answer 8

set \[.7=(\frac{1}{2})^{\frac{t}{900}}\] and solve for t

Answer 9

\[ln(.7)=\frac{t}{900}\times ln(\frac{1}{2})\]

Answer 10

\[t=\frac{900ln(.7)}{ln(\frac{1}{2})}\]

Answer 11

if you want to do it the first way using
\[Q=Q_0e^{rt}\] then first you have to solve for r, then set the result equal to 1/2 and solve for t. it will work and you will get the same answer, but it is extra work

Answer 12

ok. i see thank you

Answer 13

imaram started the problem for you but you still have to solve for r, replace it in the equation, set = to 1/2 and then solve for t.