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).