Thread: Half Life of Radon Gas

I'm working on a study sheet for an upcoming quiz in brief calculus. This section concerns exponential functions.

A building is found to contain radon gas. Thirty hours later, 80% of the initial amount of gas is still present.

I need to find an equation to represent the percentage of the initial amount of radon gas present after 't' hours, and then figure out the half-life of radon gas. The problem seems pretty simple, but I keep getting confused on finding the initial condition (a) to fit into f(x)=ab^x. I found the constant multiplier, 1.8, by taking the decimal form of 80% and adding 1 to it. The part about thirty hours is tripping me up. I can't figure out if I should be solving for the time (x) or the initial condition (a).

For your equation after 30 hours

Now for the half life, find when

Spoiler:

divide both sides by

Originally Posted by pickslides

For your equation after 30 hours

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?

Well the algebra would suggest taking to both sides, but that leaves you with which maynot be that helpful.

I used a spredsheet to solve for , so use a computer or calculator.

A little mental approximation: so the half-life is a little over 90 hours.

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