love856 wrote:I can't understand how my book explains the formula for this problem or how to do it.
To learn, in general, how to set up and solve "exponential" word problems, try
here.
love856 wrote:In two years, 20% of radioactive element decays, find its half-life.
If twenty percent is gone, then how much remains? Use this percentage (as a decimal, of course) as your value for "A" in your exponential-decay equation "A = Pe
^{kt}". Since this decay requires two years, plug "2" in for "t".
Solve the resulting equation for the decay constant "k".
Now that you have the decay constant, you can find the half-life. The half-life is the time "t" required to go from 100% (that is, P = 1) to 50% (that is, A = 0.5). So plug these values into the equation, and solve for the value of t.
If you get stuck, please reply showing how far you have gotten. Thank you!