Question

A radioactive substance decays at a continuous rate of 8.6% per day. After 15 days, what amount of the substance will be left if you started with 100 mg? (a) First write the rate of decay in decimal form. r= (b) Now calculate the remaining amount of the substance. Round your answer to two decimal places

Answer 1

The initial quantity of a radioactive substance is 100 mg .The quantity of decay in the given radioactive substance in a day is 8.6 % = 0.086 of the quantity existing on the previous day so that the quantity left next day is 0.914 of the previous day.

It is the case of a geometric series with the 1^st term 100 and common ratio 0.914.

Thus, on the 15^th day, the amount of the substance that will be left is 100* (0.914)^15-1 = 100* (0.914)¹⁴ =100*0.283953182 = 28.3953182 mg or, 28.40 mg ( on rounding off to 2 decimal places).