Wednesday, May 22, 2013
We have done nothing close to finding the radioactive decay left in objects this year. We have done logarithms that were part of solving for the equation. We’ve done logarithms here inclass before the actual project. Actually I believe it was the last thing we were learning about before we started the project so it was still fresh in my mind. In the problems we did in class the Math was much easier though. We weren’t solving for radioactive decay we were just doing simple log problems. We also used exponential functions when we had to graph what we found. We couldn’t graph the other equation because it didn’t have a X or a Y. Learning how to solve for radioactive decay could be useful for someone like an archaeologist. Finding something then figuring out the radioactive decay left in it and solving. You’d be amazed how many years it’s been there. Anthropologist could also use this. They both dig up old things and study them. Archaeologists do it for science and Anthropologist do it to learn about humans.
Sunday, May 19, 2013
To figure out how long the charcoal, gloves, bread and corn had been on the hiking trail I used the equation . X being the radioactive decay left in the item and T being how long it has been there. Since the car battery was made of lead I had to use . The first item I solved for was the charcoal. In charcoal the radioactive decay was .98285 so the equation was . Since T was in a exponent I had to use Logarithms to bring it down and set it as a fraction. Now the equation is . Then I have to get T by itself, so I multiply both sides by 5730. Now the equation is . Once again I have to get T by itself so I divide the equation by so now the equation is . Now I do the actual division on a calculator and I get T= 143. So we know the Charcoal has been there for 143 years. Then we subtract 143 from 2013 and find out it was dropped in 1870. Unfortunately there aren’t many events I could find that happened in New Mexico during 1870, so I can’t know for sure how the charcoal could have got there. If I had to guess I’d say it had something to do with mining. Probably the building of the rail roads near Santa Fe. I know that in 1878 a railroad arrived in New Mexico but it bypassed Santa Fe so I’m not too sure. To find out how long the old ladies gloves have been in Santa Fe we start with again. The radioactive decay left in the gloves was .9901297 so that will be X. So far we have . We have to put in log again to bring down. Now the equation is . We have to get T by itself again so we’ll multiply the whole equation by 5730. Once you do that the equation will be . We have to get T by itself again so now we’ll divide the whole equation by . Now we have and to get T you solve this on the calculator and you get T=81.99 but we can just round it up to 82. Next we subtract 82 from 2013 and realize it was dropped in 1931. The Great Depression was happening in 1931. The owner of the gloves was probably someone who lost their home and was living on the streets, using gloves to keep warm. Next we had the bread and corn. The radioactive decay left was .977. Now the equation is . Add logarithms to bring T down and the equation is now . Multiply the equation by 5730 to try and get T by itself and the equation is now . Then we divide the equation by and the equation is now . Now just put it into a calculator and you get T=192, so the bread and corn have been in Santa Fe for 192 years. Subtract 192 from 2013 and you get 1921. Bread and corn are common foods so there wouldn’t be a particular reason why they are there. Although in 1921 there was a Pacific Hurricane that hit North New Mexico so those could have just been brushed away from someone eating. Lastly we have to find out the info on the car battery. We used a slightly different equation for it because it has a different half life. The equation is since the half life of lead is 21 years. The radioactive decay left in the car battery was .57057 so now the equation is . Put in logarithms and the equation is now . Try and get T by itself again by multiplying the whole equation by 21. Now the equation is . Next divide the whole equation by and turn the equation into . Divide the whole thing on a calculator and get T=17. Subtract 17 from 2013 and discover the car battery was left in 1996. I would say the car battery is there because someone probably left their car up there and it was srripped of it’s parts and dropped. Just pure vandalism. There isn’t one specific landmark or something that happened in New Mexico that validates why the car battery was left there. It is anyone’s guess. But not we have solved every item. To graph these items we’ll need to turn them into exponential functions. To turn into a exponential function you have to find an A,B, and an X. A is 1 B is 0.5 and X is X/21. So to graph the charcoal, gloves, bread, and corn you put in . To graph the car battery it’s the same thing except the half life so you just swat 21 in and 5730 and the equation is . Now the difference between these equations and the one we started with is there these are way easier to graph. The exponential functions are mainly for graphing and it only gives you two points and you usually solve for A. The original function is just for solving for T.
Bread & Corn
Friday, May 17, 2013
I started this problem by asking Carl for help. I asked him what numbers went where for the equation we were to use. After that cleared up I thought I just had to solve for T. Turned out that was wrong. After that I didn’t know what to do. Carl said I had to use logarithms but I was still confused. I didn’t know how to integrate Log or how it would solve the problem. Then May came over to my table and helped me out. She explained to me why we had to use Log and showed me how to do it. She did one problem on my paper so I could have something to look at to remember how to do it. I based all the other problems from the one May did. Copied the steps and looked for T which was the amount of time the object had been there. Then I subtracted that from 2013 to know what year the object was placed or dropped there. From that year I will look into what happened at that time to come up with a logical explanation to how it got there. I couldn’t use the same equation for all of the objects because the car battery was lead based so the effect radioactive material had was different. So I used a different equation there. At this point I thought I was done, but I was nowhere near. I went to Carl to ask for a Math Check but he said we needed to find a logarithm equation to graph the objects. Since we only needed two different equations I thought it was going to be easy, it wasn’t. Me, May, and Rakeen all got together to work on it together and none of us got it. We went to Carl a couple times each during class but we never got it. So we spent two days like these just trying to figure out how to get the logarithm equation. We were getting nowhere during class so I went to ask for more help during lunch. There he explained to me how to get the equation and why it was right. Then I showed May and Rakeem and we found the Car Battery equation later. Then we just graphed both equations and we got our Math Check. In the graphs we showed time passed by and radioactive material left. Now I have to figure out how the objects got there and I believe I will be done.
Tuesday, May 7, 2013
Mr. Wild went on a trip to New Mexico with some friends. While in New Mexico Mr. Wild and his friends decide to go on a hike. During the hike they discover several unusual items such as: a car battery, old cotton lady’s gloves, charcoal, a piece of corn, and bread. My task is to discover how long the things have been there. The bread and corn had 97.7% of radioactive material left. The gloves had 99.01297% left, the car battery was lead based and had 57.057% left, and the charcoal had 98.285% left. I will use the generic formula of A(base of t)/A(base of 0)= 0.5^(t/t0.50) to measure the amount of radioactive material left in each object. t0.50 is the half life in each object. Since all the objects are made of the same thing they all have the same half life of 5730 years, except the car battery which is lead based that has a half life of 21 years. When I find out this data I will make a table,graph, and an exponential function to represent all the items and the car battery. Then I'll find out how the objects got there. I will assume it was natural disaster and look for something that happened in New Mexico during the time the object was first dropped.