Calculus
posted by Z32 .
[Exponential growth & decay]
The halflife of radioactive strontium90 is approximately 29 years. In 1965, radioactive strontium90 was released into the atmosphere during testing of nuclear weapons, and was absorbed into people's bones. How many years does it take until only 14 percent of the original amount absorbed remains?
time= ____ years

Many mathteachers use base e for most exponential problems of this type, but since "halflife" is involved, let's use 1/2 as the base
amount = a(1/2)^(t/k) or
amount = a(2)^(t/k) where a is the initial amount, t is the time in years, and k will be 29
so we have to solve
.14 = 1(2)^(t/29(
take the ln of both sides
ln .14 = t/29(ln 2), hope you know your log rules
t/29 = ln .14/ln 2
t/29 = 2.8365
t = 82.26 years.
check: after 29 years, we have 50% left
after 58 years we have 25% left
after 87 years we would have 12.5% left.
our answer appears reasonable.