# The initial mass of a radioactive goo is 180 grams. After 195 minutes, the sample has decayed to 2.8125 grams. Find the half-life of the substance in minutes? Find a formula for the amount, G(t), remaining at time t.? Find grams remain after 35 min?

##### 1 Answer

We know that a form of the decay formula is:

Where

Given

Substitute the above into equation [1]:

Solve for half-life,

Divide both sides by

Take the natural logarithm of both sides:

Use the property of logarithms that allow one to move the exponent to the outside as a coefficient:

Multiply both sides by

Divide both sides by

The formula for

The amount of the 180-gram sample remaining after 35 min: