Question

Cobalt-60 has a half-life of about 5 years. How many grams of 300 g sample well remain after 20 years?

Answer 1

20/5 = 4 half lives

so 

300 * (1/2)^4
= 300 * 0.0625
=18.75 grams

Answer 2

Answer:

After 20 years 18.75 gm of sample will remain.

Step-by-step explanation:

This is the case of an exponential decay of Cobalt-60. The function for exponential decay is,

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

where,

y(t) = amount left after time t  

a = initial amount = 300 g

r = rate of decay = 0.5 (as the sample is getting halved each time)

t = number of periods = $\dfrac{20}{5}=4$ (as we have to convert the period in terms of half lives)

Putting the values,

$y(t)=300(1-0.5)^4=300(0.5)^{4}=\dfrac{75}{4}=18.75\ gm$