Please help me solve this word problem: A certain radioactive element decays at a rate of 4% per year. Find the half-life of the substance (i.e. the time it will take for one half of any given amount of the substance to decay).
Let be the original amount
After 1 year only 96% will remain, which will be
After 2 years only 96% of will remain, which is
After 3 years only 96% of will remain, which is
...
After n years only 96% of will remain, which is
We want to know how many years before what will remain will be only or
Divide both sides by A
Take logs of both sides:
Use the rule of logs that says to bring
the exponent n in front of the log
Divide both sides by
or 17 years, rounded to the first whole year that the amount will be
no more than half the original amount.
Edwin