## anonymous 5 years ago 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?

1. anonymous

A=A0 e^rt

2. anonymous

1/2 = e^r(900)

3. anonymous

solve for r

4. anonymous

can you continue and show work

5. anonymous

$e^{900r}=1/2$ 900 r ln e= ln 1/2 900 r= ln 1/2

6. anonymous

i have an idea

7. anonymous

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

8. anonymous

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

9. anonymous

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

10. anonymous

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

11. anonymous

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

12. anonymous

ok. i see thank you

13. anonymous

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.