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

##### 1 Answer

Jul 31, 2016

Approximately

#### Explanation:

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

#0.902^t#

To find the half life we want to find

#0.902^t = 0.5#

Taking logs of both sides, we have:

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

Hence