At the beginning of an experiment, a scientist has 156 grams of radioactive goo. After 210 minutes, her sample has decayed to 2.4375 grams.

Question

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

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

How many grams of goo will remain after 35 minutes?

Answer 1

G(0) = 156 <--- this is the initial value G0

G(210) = 2.4375

G(t) = 156*(1/2)^(t/h) where h is the half life

2.4375 = 156*(1/2)^(210/h)

0.015625 = (1/2)^(210/h)

takes the log of both sides, using change of base formula:

log_1/2(0.015625) = log(0.05625)/log(1/2) = 6

6 = 210/h

6h = 210

h = 210/6 = 35

the half life is 35 minutes

G(t) = 156*(1/2)^(t/35)

there will be 78 grams left after 35 minutes.