## anonymous 5 years ago Is 1563 years the right answer? 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

we start with the formula $A=A_0(\frac{1}{2})^{\frac{t}{900}}$

2. anonymous

that formula is because you know the half life is 900

3. anonymous

then whatever you started with you will have 70% = .7 of it when you are done so set $.7=(\frac{1}{2})^{\frac{t}{900}}$ and solve for t

4. anonymous

take the log of both sides to get $ln(.7)=\frac{t}{900} ln(.5)$

5. anonymous

solve for t via $t=\frac{900ln(.7)}{ln(.5)}$

6. anonymous

i get 463 rounded but i could have made a mistake

7. anonymous

oh. that is an avail answer. i was way off..haha

8. anonymous

whew

9. anonymous

ok. thanks