In 2015 the initial amount of a radioactive substance is 100

In 2015, the initial amount of a radioactive substance is 100 grams and is decreasing exponentially at a yearly rate of 10 %. In what year, will there be half of the substance left?

Solution

We have to use the following formula

P(t)= P₀(1-r)^t

P(t) is the amount after t years which is half of 100 gms=50 gms

P₀ is the initial amount which is 100 gms here

r is the interest rate which is 10%=.1

50=100(1-.1)^t

.5= .9^t

Taking log on both sides

log .5/log.9=t

t=6.6 yrs

Therefore in year 2021,half of the substance left