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

Answer:

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

Step-by-step 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.

$T = \frac{300}{10}$

$T = 30$

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

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

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

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