how many half-lives have passed if only 1/16 of the original amount of the element remains? a-two b-three c-four d-five

To determine the number of half-lives that have passed if only 1/16 of the original amount remains, we can use the formula:

Remaining amount = (1/2)^(number of half-lives) * Original amount

In this case, the remaining amount is 1/16, and we want to find the number of half-lives. So we can rewrite the formula as:

1/16 = (1/2)^(number of half-lives) * Original amount

To simplify the equation, we can substitute the original amount with 1 (since it remains constant in this case):

1/16 = (1/2)^(number of half-lives)

Now, we need to determine the power to which 1/2 must be raised to obtain 1/16. We can rewrite 1/16 as 2^(-4) (using the fact that 2^(-4) is equal to 1/2^4 = 1/16).

So now we have:

1/2^4 = (1/2)^(number of half-lives)

Comparing the exponents, we can conclude that the number of half-lives is 4. Therefore, the answer is c) four.