Carbon dating word problem
Most scientists and many Christians believe that the radiometric dating methods prove that the earth is 4.5 billion years old.
The textbooks speak of the radiometric dating techniques, and the dates themselves, as factual information.
Familiar to us as the black substance in charred wood, as diamonds, and the graphite in “lead” pencils, carbon comes in several forms, or isotopes.
One rare form has atoms that are 14 times as heavy as hydrogen atoms: carbon-14, or C ratio gets smaller.
C) dating usually want to know about the radiometric dating methods that are claimed to give millions and billions of years—carbon dating can only give thousands of years.
People wonder how millions of years could be squeezed into the biblical account of history. Christians, by definition, take the statements of Jesus Christ seriously.
Hi--welcome back to 0000Today we are going to talk about applications of exponential and logarithmic functions.0002At this point, we have a good understanding of exponentiation and logarithms.0007In this lesson, we will see some of the many applications that they have.0010Exponential and logarithmic functions have a huge array of applications.0013They are used in science, in business, in medicine, and even more fields.0017They are used in all sorts of places.0021There are far too many applications to discuss them all in this lesson, so instead we will focus on working a variety of examples.0024We will begin with a brief overview of some other uses--some of the uses that we can see for exponential functions and logarithmic functions.0029Then, we will look at many specific examples, so we can really get our hands dirty and see how word problems in this form work.0035Now, before you watch this lesson, make sure you have an understanding0040of exponents, logarithms, and how to solve equations involving both, before watching this.0043We won't really be exploring why the actual nuts and bolts of this solving works--how these things work.0048We are just going to be launching headfirst into some pretty complicated problems.0053So, you really want to have an understanding of what is going on, because we are going to hit the ground running when we actually get to these examples.0057Previous lessons will be really, really helpful here if you are not already used to this stuff.0062OK, let's go: applications of exponential functions: exponential functions allow us to describe the growth or decay0066of a quantity whose rate of change is related to its current value.0073So, how fast it is changing is connected to what it is currently at.0078So, some examples of applications: we can also see how their rate of change is related to its current value:0083Compound interest--the amount of interest that an account earns is connected to how much money is already in the account.0088If you have ten thousand dollars in an account, it will earn more than if it has one thousand dollars in the account,0096or than if it has one hundred dollars in the account.0101So, this is an example of seeing how the rate of change is related to the current value of the object.0103Other things that we might see: depreciation--loss in value; compound interest and loss in value0109are both used a lot in banking and business--anything that is fiscally oriented.0114Population growth is used a lot in biology; half-life--the decay of radioactive isotopes--shows up a lot when we are talking about physics.0118If you are studying anything in radiation, understanding half-life is very useful.0127And many others--there is a whole bunch of stuff where exponential functions are going to show up.0131It is really, really useful stuff.0135Now, I have a secret for you: don't let anybody else know about this.0138Many exponential functions have their own formula--things like compound interest, 1 plus the number of times that it compounds in a year, divided...0142Oh, this should actually be the other way around; it should not be n/r; it should r/n.0152The rate of it, divided by the number of times it compounds, to the number of times it compounds, times the time--0160if you don't remember that one, remember our very first lesson on exponential functions that described why that is the case.0167Population doubling is P, some original starting principal amount, times 2 to the rate that they double at, times t.0173Half-life is some principal starting amount times 1/2 to the rate times time.0181However, if you forget all of these formulas--there are a bunch of different formulas;0187there are even more than just these; but it is sometimes possible to use the natural exponential growth model.0191You can sometimes swap out any one of these more difficult-to-remember ones for simple "Pert"--0197P, the original starting amount, times e, the natural base, to the r times t,0205where r is the rate of the specific thing that we are modeling, times time.0210r will change, depending on what different thing you are doing.0214So, even if you are modeling isotopes--half-life in plutonium and half-life in uranium--you will get very different r's,0217because the plutonium and uranium will have different rates of decay.0222So, you are not going to use the same rate r.0226Once again, if you are talking about half-life, the r here would be totally different than the r in our Pe form from the problem, you can get away with using it instead.0246There are many situations where you might not remember any one of these specialized formulas.0255But it can be OK if you have enough information from the problem to be able to figure out what r has to be.0260There are lots of cases where that will end up being the case.0266We will talk about a specific one on Example 2; we will see something where we could get away with not knowing0269the specific formula, and still be able to figure things out by using this Pe formula.0275We will talk about it in Example 2, if you want to see a specific example of being able to use this secret trick.0279Why is this the case?