At the beginning of an experiment, a scientist has 200 grams of radioactive goo. After 255 minutes, her sample has decayed to 3.125 grams.

Question

At the beginning of an experiment, a scientist has 200 grams of radioactive goo. After 255 minutes, her sample has decayed to 3.125 grams.

What is the half-life of the goo in minutes? 

Find a formula for G(t) the amount of goo remaining at time t. G(t)=?

How many grams of goo will remain after 20 minutes? 

Answer 1

200 g then after 255 minutes down to 3.125 grams

what is the half life in minutes

G(0) =200 at zero minutes

G(255) =3 1/8=25/8 after 255 minutes

200(.5)^x= 25/8=3.125

.5^x=25/8/200=1/64

.5^6=1/64

x=6 half lives in 255 minutes

.

half life

0 200'

1 100'

2 50'

3 25'

4 12.5

5 6.25

6 3.125

255 minutes = 6 half lives

one half life= 255/6 = 42 1/2 minutes

G(42.5)=100=200(1/2)^1

G(t)=200(1/2)^(t/42.5)

G(20)= 200(1/2)^(20/42.5)=about 143 1/3 grams of goo after 20 minutes