Tritium (half-life = 12.3 y) is used to verify the age of expensive brandies. If an old brandy contains only the following fraction of the tritium present in new brandy, how long ago was it produced?

1/16

(1/2)^x=1/16

12.3x=?

i don't think it 4

x=4

12.3(4)=?

1/16 = (1/2)^4 so four half lives

4 * 12.3 as TutorCat said

To determine how long ago the old brandy was produced based on the fraction of tritium present, we need to use the concept of half-life.

The half-life of tritium is given as 12.3 years, which means that every 12.3 years, half of the tritium in a sample will decay.

In this case, the old brandy contains only 1/16th of the tritium present in new brandy.

Since we know that half of the tritium decays every 12.3 years, we can determine the number of half-lives that have occurred by finding the exponent that results in 1/16 when raised to that power.

1/2^x = 1/16

To solve for x, we can take the logarithm of both sides of the equation. Using the logarithm base 2 (because we have a power of 2 involved), we get:

log₂(1/2^x) = log₂(1/16)

Applying the logarithm property that shifted the exponent to the front, we have:

-x * log₂(1/2) = log₂(1/16)

The logarithm base 2 of 1/2 is -1, so the equation becomes:

-x * (-1) = log₂(1/16)

Simplifying further, we have:

x = log₂(16)

Using the logarithm base 2 identity, we know that 2^4 = 16. Therefore, log₂(16) = 4.

Thus, x = 4, which means that 4 half-lives have occurred.

Finally, we can determine the age of the old brandy by multiplying the number of half-lives by the half-life of tritium:

Age = 4 * 12.3 years = 49.2 years

Therefore, the old brandy was produced approximately 49.2 years ago.