Question

A sample of radium has a weight of 1.5 mg and decays

by half every 6 years. Circle all of the following
functions that correctly model the amount of radium
f(t) in mg remaining after t years

Answer 1

Answer:
`(b)`

Explanation:

Given

Initial mass of radium is
`A_o=1.5\ mg`

It decays by half every 6 years i.e.
`T_{(1)/(2)}=6`

For radioactive decay, sample at any time is given by

`\Rightarrow A=A_o2^{-\frac{t}{T_{(1)/(2)}}}`

Insert the values

`\Rightarrow A=1.5\cdot 2^{(-t)/(6)}\\\\\Rightarrow A=1.5\cdot \left((1)/(2)\right)^{(-t)/(6)}\\\\\Rightarrow A=1.5\cdot (0.5)^{(t)/(6)}`

Thus, option (b) is correct.