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.

Question

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.

anonymous · Answer

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

anonymous · Answer

that formula is because you know the half life is 900

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

i get 463 rounded but i could have made a mistake

anonymous · Answer

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

anonymous · Answer

whew

anonymous · Answer

ok. thanks