Need help with half-life question

[KarenNC]

Here's the question (from biology):

3. Uranium­238 decays into lead. For a given amount of 238U, half is converted to lead every 4.5 million years.

a) If a sample is found with 1/8 (0.125) of the expected 238U, how old would this sample be? (2 points)

 

Now, using A for the beginning amount and with my current understanding of the process, it would work out as follows:

A begin count

1/2 A 4.5 million years (one half-life)

1/4 A 9 million years (two half-lives)

1/8 A 13.5 million years (three half-lives)

 

So, three half-lives, so the sample would be about 13.5 million years old. Other examples online I've looked at for similar problems seem to follow this pattern. The answer given in the key, however, says that it would be three half-lives, but about 18 million years old. Is the answer key in error, or have I missed an important step?

[Arcadia]

13.5 million years is correct

The same radioactive decay is taught in physics. I actually calculated using the generic natural log radioactive formula for fun.

 

You can input at below link and get the same answer. You just need to choose Uranium 238

https://www.ehs.washington.edu/rso/calculator/activity_calc.shtm

 

ETA:

Example of a typical radioactive decay graph

http://www.launc.tased.edu.au/online/sciences/PhysSci/done/nuclear/decay/Decay.htm

 

ETA:

Weird thing is U238 is listed as having a half life of 4.5 billion years at some sites like Duke and USGS

http://pubs.usgs.gov/gip/geotime/radiometric.html

http://people.chem.duke.edu/~jds/cruise_chem/nuclear/chemwindow/halflife.html

[KarenNC]

Thanks!