Question

At the beginning of an experiment, a scientist has 132 grams of radioactive goo. After 135 minutes, her sample has decayed to 8.25 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 47 minutes

Answer 1

Answer:

• 33.75 minutes
• G(t) = 135(1/2)^(t/33.75)
• 51.42 grams

Step-by-step explanation:

Based on the given numbers, we know the decay factor is ...

  8.25/132 = 1/16

in 135 minutes. We recognize 1/16 = (1/2)^4, so is 4 half-lives.

a) The half-life of goo is (135 min)/4 = 33.75 minutes

__

b) A formula for the amount remaining could be ...

  G(t) = 135(1/2)^(t/33.75)

__

c) After 47 minutes, the amount remaining is ...

  G(47) = 135(1/2)^(47/33.75) ≈ 51.42 . . . grams

_____

Comment on the solution

The general form of a decay equation can be ...

  g(t) = (initial value)(decay factor)^(t/(decay time for the given factor))

For our G(t), we used a decay factor of 1/2 and the half-life time of 33.75 minutes.