IM lost and this hw is due soon please help

Question

At the beginning of an experiment, a scientist has 212 grams of radioactive goo. After 135 minutes, her sample has decayed to 26.5 grams.

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

Find a formula for , the amount of goo remaining at time .   _____

How many grams of goo will remain after 2 minutes?  _____

Answer 1

Standard formula:

G(t) = G₀(t) (0.5)^(t/t_hf)

Given Data:

G₀(t) = 212 grams

t = 135 minutes

G(t) = 26.5 grams

Rewrite Standard Formula:

t_hf = log 2 (t) / log(G₀(t)/G(t))

Input Given Data:

t_hf = 45 = HALF LIFE

NEW FORMULA

G(t) = 212 (0.5)^(t/45)

Goo Remaining after 2 minutes:

G(t) = 212 (0.5)^(2/45) = 205.568586665

The problem is poorly written and I assumed that when asking for the amount of goo remaining after 2 minutes, that we start with the initial 212 grams.

Answer 2

Mass decreases by half, every halflife

So after 1 halflife mass is 212 / 2 = 106 g

After 2 halflives, 106/2 = 53 g

After 3 halflives, 53/2 = 26.5 g

So 3 halflives must be 135 minutes, so 1 halflife = 135/3 = 45 mins

After t minutes G(t) = 212 (0.5)^t/45

212 = initial amount (g)

45 = halflife (minutes)

So after 2 minutes G(2) = 212 (0.5)^2/45