Question

he half-life of a certain radioactive substance is 14 days. There are 6.6 grams of the substance present initially. Which equation represents the number of grams of the radioactive substance on day 42 ?

Answer 1

Answer:

First one

Step-by-step explanation:

The first one  

y = 6.6 (1/2 ) ^n     where n = the number of half lives

                                42 days/ 14 days/halflife  = 3 halflives

Answer 2

Answer:

$y=6.6(0.5)^3$

Step-by-step explanation:

half-life of 14 days, basically means it reduces by 50% or half every 14 days.

This can generally be expressed as: $f(x)=a(0.5)^{\frac{t}{h}}$, where h=half life, and t=time, where the unit of time for t and half-life is the same. also a is the initial value.

So we can express this half-life equation as: $f(x)=6.6(0.5)^{\frac{t}{14}}$ where t=days.

So plugging in 42 days in here, we get: $f(x)=6.6(0.5)^{\frac{t}{14}} = 6.6(0.5)^3$

The reason for this is because 42 days is 3 half-lives.