When scientists analyze a rock for its age they are able to determine what events occurred and how it affected life. what do scientists deduce from this? a. determine which fossils are more dense b. determine soil settling rates on earth c. that life on earth has stayed the same d. over time life on earth has changed

Geologists use two techniques to date rock layers. The first technique is called "relative dating." If one layer of rock lies above another, we can regard the upper layer as younger, particularly when the layers are relatively horizontal and do not show faulting. When one finds layers at an angle, especially at a sharp angle, one can regard the formation as due to shifts in the earth that occurred after the layers were deposited. When one sees that one kind of rock cuts across layers of other kinds of rock, one can regard the intruding rock material as younger. Rock material enclosed in another kind of rock material can be regarded as older than the enclosing material. 
Relative dating is basically studying the layers of rock exposed at a site and making common-sense inferences about how the layers could have been formed so as to produce the layering one sees. 

Relative dating does not allow one to assign a numerical age to a rock formation. 

Radiometric dating does allow estimation of a numerical age for a rock formation. To carry out radiometric dating, one studies the quantities of specific isotopes of radioactive elements relative to the specific isotopes of the elements into which the radioactive elements decay. For example, uranium 235 decays into lead 207. We know the half-life of uranium 235. So, if we find that the amount of U-235 is equal to the amount of lead 207, we can regard the rock as being about as old as the half-life of uranium, which we know to be on the order of 700 million years. In other words, when the rock we're studying solidified, the uranium was captured within it. The uranium then turned into lead at a known rate, which also remained captured in the solid rock until we came along and examined it. Knowing the rate allows us to calculate the length of time the uranium has been sitting in the rock. 

Needless to say, the actual process involved in applying this concept has its complexities. However, this is the basis of the procedure. By examining large numbers of rock formations, using both relative and radiometric dating, we can work out the patterns that govern the formation of rock layers. By comparing large numbers of sites to each other, we can learn to see that the rocks at one site have the same characteristics as the rocks at another site. Just as we learn to estimate the ages of people by indirect means, such as skin texture, hair color, posture, voice, and even attitude, we learn to recognize that at a given site, the rock layers show the same characteristics as other rock layers of known age. We can thereby infer the age of rock layers at a site where something prevents us from analyzing the rocks directly. 

Fossils found in rocks can be useful for determining the age of rocks. From a variety of sources quite independent of rock geology, we know how old some fossils are. When we find such fossils in rock, we can use the fossils as a clue to the age of the rock. In like manner, when we find fossils of unknown age embedded in rock of known age, we can infer the age of the fossils. Of course, as anyone with common sense would realize, we cannot determine both the age of a fossil and the age of the rock around it from each other. We have to compare both specimens to other specimens of known age, and apply, if possible, techniques such as radiometric dating to determine the age of the material we're examining.