The half-life of a radioactive substance is the average amount of time it takes for half of its atoms to disentegrate. suppose you started with 200 grams of a substance with a half-life of 3 minutes. how may minutes have passed if 25 grams now remain? explain your reasoning.

To solve this, we are going to use the formula: 
where:
the final amount of the substance 
is the initial amount of the substance 
is the time 
is the half life

We know from our problem that , , and . Lets replace those values in our formula:



Notice that  is in the exponent, so we must use logarithms to bring it down:







We can conclude that 9 minutes have passed after the substance started  to decay for you to have 25 gr of the substance remaining.

Subtracting is the opposite of adding