At the beginning of an experiment, a scientist has 224 grams of radioactive goo.

Question

At the beginning of an experiment, a scientist has 224 grams of radioactive goo. After 105 minutes, her sample has decayed to 7 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 17 minutes?

Answer 1

7 = 224×(1/2)^105/h

Divide both sides by 224:

(7/224) = (1/2)^105/h

Take the log base (1/2) of both sides:

log _(1/2) [7/224] = 105/h

h = 105 / log _(1/2) [7/224] = 105/5

= 21 minutes, the half-life.

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In 7 minutes,

x = 224 * (1/2)^t/h = 224 * (1/2)^7/21

x = 224 * (1/2)^1/3

x = 177.79 grams, approximately.