The dating math problem
The task requires the student to use logarithms to solve an exponential equation in the realistic context of carbon dating, important in archaeology and geology, among other places.
Students should be guided to recognize the use of the logarithm when the exponential function has the given base of $e$, as in this problem.
However, I note that there is no beginning or ending amount given.
How am I supposed to figure out what the decay constant is?
Eventually, the salt water will eat through the steel and release the Plutonium (which, as you know, is quite lethal.) They usually talk about either trying to raise the sub or encase it in concrete where it rests. That's why we are called "Carbon-based life forms." Man, I've really watched too much Star Trek.)Scientists use Carbon-14 to make a guess at how old some things are -- things that used to be alive like people, animals, wood and natural cloths. Anyway, they make an estimate of how much Carbon-14 would have been in the thing when it died...
The last figure I heard was that there are currently eight nuclear subs on our ocean floors. It doesn't work for sea creatures and other things that are under water. Then they measure how much is left in the specimen when they find it.
There is a so-called rule about dating: the youngest age you are supposed to date is half your age plus seven.So, if you’re 16, the youngest age you should consider is 15 — because 16 divided by two is eight and 8 7 equals 15.We can write the dating rule as an equation: $y=x \div 2 7$.If possible, the ink should be tested, since a recent forgery would use recently-made ink.Two things: the somewhat random-looking picture above is from The Moon Is Blue, a 1953 film that’s the first known reference to the ‘dating rule’ discussed here.Carbon 14 is a common form of carbon which decays over time.The amount of Carbon 14 contained in a preserved plant is modeled by the equation $$ f(t) = 10e^.Furthermore, since the maximum frequency is 12 and there are 12 months in the year the second assumption is true (for this equation).While this does answer the main question, a few sub questions arose.After 5600 years, if we start with a gram, we end up with half a gram.This rather complex formula shows you how to solve this puzzle using accepted scientific methods.