Question

A radioactive substance decays at a rate of 25% every 10 years. Which equation represents the amount of the substance (S) remaining from 100 grams after 300 years?

Answer 1

`y = 100 * (0.75)^{30`

Explanation:

Given

`a =100` --- Initial Amount

`r= 25\%` every 10 years

Required

The remaining amount after 300 years

To do this, we make use of:

`y = a(1 - r)^T`

Where

r = decay rate

T = the period of decay

In 300 years, there are 30 periods of 10 years.

i.e.

`T = (300)/(10)`

`T = 30`

`y = a(1 - r)^T`

`y = 100 * (1 - 25\%)^{30`

`y = 100 * (1 - 0.25)^{30`

`y = 100 * (0.75)^{30`