The decay rate of a certain chemical is 9.8% per year what is the half life?

Question

5434 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-31T22:27:01

Approximately #6.72# years

The proportion left at the end of one year is:

#(100-9.8)/100 = 90.2/100 = 0.902#

The proportion left at the end of #t# years will be:

#0.902^t#

To find the half life we want to find #t# such that:

#0.902^t = 0.5#

Taking logs of both sides, we have:

#t log(0.902) = log(0.902^t) = log(0.5)#

Hence #t = log(0.5)/log(0.902) ~~ 6.72# years