At the beginning of an experiment, a scientist has 172 grams of radioactive goo. After 270 minutes, her sample has decayed to 5.375 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 t. G(t)= 

How many grams of goo will remain after 74 minutes?

Answer 1

T = half-life in minutes

 

T must satisfy

 

5.375 = 172 (0.5)^270/T

 

0.03125 = (0.5)^270/T

 

log(0.03125) = (270/T) log(0.5)

 

T = 270 log(0.5) / log(0.03125) = 54 minutes

 

G(t) = G₀ (0.5)^t/54,

 

with t in minutes and 

 

G₀ = 172 g

 

G(t) = 172 (0.5)^t/54

 

G(74) = 172 (0.5)^174/54 g = ? g