In 2008 the initial amount of a radioactive substance is 100

In 2008, the initial amount of a radioactive substance is 100 grams and Find the amount of the radioactive substance in year 2024. In what year will there be half of the substance left?

Solution

We have to use the following formula

A= A₀(1-r)^t

A is the amount left after t years

A₀ is the initial amount

A= 100(1-.09)¹⁶= 100(.91)¹⁶= 22.11gms

b. half of the amount left means half of 100 that is 50gm

50=100(1-.09)^t

.5=.91^t

Taking log on both sides

log .5= t log .91

t=log.5/log.91=7.35 years that is approx 7 years 4 months from 2008 , that is in year 2015