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

First one

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

`y=6.6(0.5)^3`

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)^{(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)^{(t)/(14)}` where t=days.

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

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