Re: Half Life of Radon Gas

For your equation $\displaystyle f(x)=ab^x$ after 30 hours $\displaystyle 0.8\times a=ab^{30} \implies 0.8=b^{30}\implies b= 0.9926$

Now for the half life, find $\displaystyle x$ when $\displaystyle \frac{a}{2}=a\times 0.9926^x $

Re: Half Life of Radon Gas

Quote:

Originally Posted by

**pickslides** For your equation $\displaystyle f(x)=ab^x$ after 30 hours $\displaystyle 0.8\times a=ab^{30} \implies 0.8=b^{30}\implies b= 0.9926$

I'm confused at this point, and I think I'm misunderstanding a piece of algebra. Did you take the log of both sides? How were you able to evaluate the b^30?

Re: Half Life of Radon Gas

Well the algebra would suggest taking $\displaystyle \log_b$ to both sides, but that leaves you with $\displaystyle 30 = \log_b0.8$ which maynot be that helpful.

I used a spredsheet to solve for $\displaystyle b $ , so use a computer or calculator.

Re: Half Life of Radon Gas

A little mental approximation: $\displaystyle 0.8=b^{30}\Rightarrow 0.8^3=0.512=b^{90}$ so the half-life is a little over 90 hours.

Re: Half Life of Radon Gas

Thanks for the help, I guess I just needed to play around with the numbers a bit.