An unknown radioactive element decays into non-radioactive substances. In days the radioactivity of a sample decreases by percent.
(a) What is the half-life of the element?
Read this thread: http://www.mathhelpforum.com/math-he...ive-decay.html
You have to do the same sort of thing.
initial amount of substance, $\displaystyle A_0 = x$
final amount of substance, $\displaystyle A_N = x - 0.75x = 0.25x$
time, t = 980 days
half life = h = ?
$\displaystyle A_N = A_0 \left(\frac{1}{2}\right)^{\frac{t}{h}}$
$\displaystyle 0.25x = x \left(\frac{1}{2}\right)^{\frac{980}{h}}$
$\displaystyle 0.25 = \left(\frac{1}{2}\right)^{\frac{980}{h}}$
$\displaystyle \left(\frac{1}{2}\right)^2 = \left( \frac{1}{2} \right)^{\frac{980}{h}}$
$\displaystyle
2 = \frac{980}{h}$
h = 490 days