Question

A radioactive substance decays by x % each day. After 8 days half of the substance has decayed. Find the value of x. Give your answer to 1 decimal place.

Answer 1

8.3

Explanation:

Let Ao be the original amount and A the amount after t days.

Then we have the exponential function

A = Ao(1 - x)^t or

A/Ao = (1 - x)^t

When t = 8, A/Ao = 0.5

0.5 = (1 - x)^8

(0.5)^(1/8) = 1 - x

0.917 = 1 - x

x = 1 - 0.917 = 0.083 = 8.3 %

The substance decays by 8.3 % each day.