Question

At the beginning of an experiment, a scientist has 292 grams of radioactive goo. After 60 minutes, her sample has

decayed to 9.125 grams.

Answer 1

The halflife of goo is 12 minutes

Explanation:

Use formula

`A=A_0\cdot \left((1)/(2)\right)^{(t)/(k)}`

In your case,

`A_0=292\\ \\A=9.125\\ \\t=60`

Find k:

`9.125=292\cdot\left((1)/(2)\right)^{(60)/(k)}\\ \\ \left((1)/(2)\right)^{(60)/(k)}=(9.125)/(292)\\ \\ \left((1)/(2)\right)^{(60)/(k)}=0.03125\\ \\ \left((1)/(2)\right)^{(60)/(k)}=(1)/(32)\\ \\ \left((1)/(2)\right)^{(60)/(k)}= \left((1)/(2)\right)^(5)\\ \\(60)/(k)=5\\ \\5k=60\\ \\k=12`

The halflife of goo is 12 minutes