Numerical sequences

Identify numerical patterns to determine the next three terms in an addition or subtraction sequence.

Represent problems using an input-output table and numerical expressions to generate a number pattern that follows a given rule representing the relationship of the values in the resulting sequence and their position in the sequence

Earth's History. All the processes that have been discussed require long periods of time to create a noticeable change on Earth's surface. You can just imagine how long it would take to create an oceanS as vast as the Pacific Ocean if the ocean floor moves only at about 10 cm/year. It is then important to know the history of Earth to learn the complexities of its past and be able to use it to understand the present. Just like learning the history of a country that requires one to read a lot of books, learning the history of Earth involves studying a lot of rocks. Rocks, especially sedimentary rocks, contain a lot of information about Earth's past. It holds the key to most of the geologic processes that happened on Earth and the key to uncovering how life on Earth evolved. But these discoveries are worthless if there is no time perspective. Thus, one of the most important contributions of geologists to mankind is the geologic time scale, which holds a history that is exceedingly long.The geologic time scale divides the history of Earth into different blocks of time by using relative dating. Since geologists use rocks to understand Earth's history, dating does not give accurate numerical dates, it only tells that an event preceded the relative dating places these rocks in their proper sequence of formation. But relative other. This method is still widely used today, alongside a more accurate method called absolute dating, which uses radioactive elements. With relative and absolute dating. geologists can trace the history of Earth. Relative Dating. Relative dating requires one to know the basic principles such as law of super-position, principle of original horizontality, principle of cross-cutting relationships, and unconformities.Law of Superposition The law of superposition is the most basic principle in relative dating. It states that in an undeformed sequence of sedimentary rock, the layers found at the top are the youngest rocks and the layers at the bottom are the oldest. It may seem too obvious, but this principle has only been clearly stated in 1669 by the Danish anatomist, geologist, and priest, Nicolaus Steno. Principle of Original Horizontality Along with the law of superposition, Steno stated that an undeformed sequence is the one where the layers are still in a horizontal position. This follows the principle of original horizontality, which states that sediments are deposited horizontally. Principle of Cross-Cutting Relationships The principle of cross-cutting relationships determines which events occurred first depending on which rocks are affected. The geologic layer that cuts another is younger than the layer it cuts across.Unconformities Rock layers that have not been interrupted are considered conformable. These sites represent spans of geologic time. But there is no place on Earth that has a complete conformable stratum since external and internal processes have always interrupted the deposition of the sediments. These breaks in the record of the rock strata are called unconformities. Using unconformities, geologic events are determined. There are three basic types of unconformities angular unconformity, disconformity, and nonconformity. Angular unconformity is characterized by having tilted or folded sedimentary rocks below younger, horizontal layers of rock. Disconformity is determined where there are missing parallel rock layers. Erosion takes place and removes the younger top layers and then deposition would once again happen. Nonconformity is characterized by an igneous or metamorphic rock found below a sedimentary rock. Figure 3-13. Three basic types of unconformities Using these principles for relative dating, one can determine the order of events However, relative dating does not give a time element as to when they happened. Absolute Dating For a much more accurate method of determining the history of Earth, geologists make use of absolute dating. This method uses unstable elements to determine the exact age of rocks. Isotopes are elements that have the same number of protons but different number of neutrons. Most isotopes are stable but some may be unstable. This is because the forces that bind the protons and neutrons in the nucleus of the isotope are not strong enough to hold them together, resulting in a radioactive decay, The unstable isotopes are called radioactive isotopes or parent isotopes. When these parent isotopes undergo radioactive decay, new isotopes, known as daughter products, are formed. The time it takes for one-half of the nuclei in the sample to decay is called half-life. This amount of time is fixed for each kind of radioactive isotope no matter what physical conditions it is subjected to. The ratio of parent daughter isotope determines how many half-lives have passed. If it is 1:1, then one half-life has passed; if it is 1:3, then two half-lives have passed; and if 1:7, then three half-lives have passed, and so on. Therefore, using the concept of half-life and parent-daughter ratio, geologists can determine the exact age of the sample. This method is called radiometric dating. It uses five radioactive isotopes to determine the age of rocks. For dating rocks that are about a million years old, rubidium-87, thorium-232, and the two isotopes of uranium (U-238 and U-235) are used. The fifth radioactive isotope is potassium-40, which has a half-life of 1.3 billion years. With these radioactive elements, determining the accurate age of rocks becomes easier. For dating events that are more recent, radiocarbon dating is used. This method uses carbon-14. Carbon-14 has a half-life of 5730 years and can be used to date back events up to 75000 years. All organisms contain a small amount of carbon-14, which is proportional with the amount of carbon-12. When an organism dies, the carbon-14 decays and is no longer replaced. The amount of carbon-14 left in the sample is then compared to the amounts of carbon-12 present, and radiocarbon dates can then be determined. This method has been particularly useful for anthropologists, archeologists, historians, and geologists for events that are much more recent.Fossils Aside from rocks, geologists also use the remains of living organisms in understanding Earth's history. Some fossils are formed from parts of an organism (body fossil), while some provide signs or clues as to which life-forms were present at that time (Frace fossils). Fossils contain a lot of information about the past the kind of organisms that have lived, the environment where organisms lived, and the evolution organisms underwent as their environment changed. However, not all organisms turned into fossils, therefore, scientists cannot learn everything about the past using fossils alone. There are also fossils that are used to determine the age of a rock. These are index fossils and these are only found in rocks of a particular age. The organisms that turned into index fossils have a relatively short life-spanning from a few million years to a few hundred million years. Index fossils are also found in most of the common rocks around the world, which makes them easier to identify.The methods used for dating the age of rocks are also used for fossils. Absolute dating is more commonly used since it can give exact numerical dates for the age, but relative dating can also be used to determine which fossils are older.

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