# Math Help - Half Life Question

1. ## Half Life Question

I have an answer that I doubt (I do not have a textbook for an answer).

Here is the question: A radioactive substance has a half life of 20 days

i) How much time is required so that only 1/32 of the original amount remains?

My answer: T = 100 days?

ii) Find the rate of decay at this time.

-0.001/day?

2. Originally Posted by CuriousThought
I have an answer that I doubt (I do not have a textbook for an answer).

Here is the question: A radioactive substance has a half life of 20 days

i) How much time is required so that only 1/32 of the original amount remains?

My answer: T = 100 days?

ii) Find the rate of decay at this time.

-0.001/day?

Assume we begin with a quantity x, so after 20 days we get $\frac{x}{2}=xa^{20}\Longrightarrow a^{20}=\frac{1}{2}\Longrightarrow a=2^{-1\slash 20}$ ,and from here $\frac{x}{32}=x\left(2^{-1\slash 20}\right)^t\Longrightarrow t=\frac{-\ln(32)}{\ln(2^{-1\slash 20})}=100$ , and your answer's correct

Tonio