At the beginning of an experiment, a scientist has 128 grams of radioactive goo. After 165 minutes, her sample has decayed to 2 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 8 minutes?

Answer 1

We can use this as the half-life equation:

G(t) = G₀(1/2)^t/h

where G(t) is the amount of the substance left after time "t", G₀ is the amount at the start (at time t = 0), "t" is the amount of time that goes by, and "h" is the half-life. Note that "t" and "h" must be in the same units of time.

So, we can say:

2 = 128(1/2)^165/h

2/128 = (1/2)^165/h

log_1/2(2/128) = log_1/2(1/2)^165/h

6 = 165/h

h = 165/6

h = 27.5 minutes

You start with 128 g, after 27.5 minutes there are 64 g left, after 55 minutes there are 32 g left, after 82.5 minutes there are 16 g left, after 110 minutes there are 8 g left, after 137,5 minutes there are 4 g left, and after 165 minutes, there are 2 g left

Since you now know h = 27.5, you have the equation G(t) = 128(1/2)^t/27.5 so you can plug in t = 8:

G(8) = 128(1/2)^8/27.5 = 128(1/2)^0.29090909 = 128(0,8173868) = 104.63 grams