Question

Cobalt-60 has an annual decay rate of about 13%.

Answer 1

Answer:

Option: C is the correct answer.

                          C. 18.51 g

Step-by-step explanation:

The situation of this problem can be modeled with the help of the exponential decay function :

i.e. any component if it has a initial amount as a units and is decaying at a rate of r% then the amount after t years is given by:

$n(t)=a(1-\dfrac{r}{100})^t$

Here we have:

r=13%

and a=300 g

and t=20 years

Hence, we have

$n(20)=300\cdot (1-\dfrac{13}{100})^{20}\\\\i.e.\\\\n(20)=300\cdot (1-0.13)^{20}\\\\i.e.\\\\n(20)=300\cdot (0.87)^{20}\\\\n(20)=300\cdot 0.061714\\\\i.e.\\\\n(20)=18.5142\ g$

The amount that will be left after 20 years is:  18.51 g

Answer 2

The answer will be c