The dating math problem
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.
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.
It comes from cosmic rays that rain down on the earth (and us) from outer space.
However, I note that there is no beginning or ending amount given.
I do not have the decay constant but, by using the half-life information, I can find it.
(Since this is a decay problem, I expect the constant to be negative.
This is why it is such a big concern when a nuclear submarine sinks... (By the way, you are mostly Carbon-12, which is not radioactive.If I end up with a positive value, I'll know that I should go back and check my work.) In Its radiation is extremely low-energy, so the chance of mutation is very low.(Whatever you're being treated for is the greater danger.) The half-life is just long enough for the doctors to have time to take their pictures.Some examples of exponential growth are population growth and financial growth.The information found, can help predict what a population for a city or colony would be in the future or what the value of your house is in ten years.