Introduction to Logical Deduction, Concepts on : Logical Reasoning. Conditional notations are the symbols used to represent logical statements in a concise manner.

Let us consider two statements and : It is raining Mukesh carries an umbrella.

Welcome to CK-12 Foundation. Suppose the amount of a radioactive substance is cut in half every 25 years.

If there was originally 500 grams of the substance, could you write a function representing the amount of the substance after years? How much of the substance would there be after 100 years? Will the amount of the substance ever reach 0 grams? Exponential Decay In the last Concept, we learned how to solve expressions that modeled exponential growth. Recall that the general form of an exponential function is , where initial value and In exponential decay situations, the growth factor must be a fraction between zero and one. Composition of Functions – College Algebra. Learning Objectives In this section, you will: Combine functions using algebraic operations.Create a new function by composition of functions.Evaluate composite functions.Find the domain of a composite function.Decompose a composite function into its component functions.

Suppose we want to calculate how much it costs to heat a house on a particular day of the year.

Algebra - Finding Zeroes of Polynomials. Show Mobile NoticeShow All NotesHide All Notes You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone).

Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width. Section 5-4 : Finding Zeroes of Polynomials We’ve been talking about zeroes of polynomial and why we need them for a couple of sections now. We will need the following theorem to get us started on this process. Rational Root Theorem. Quick Method to Solve Data Sufficiency Questions – HitBullsEye. Data Sufficiency is a very important part of almost all the competitive exams, so you cannot take the risk of skipping it.

Data Sufficiency uses direct and indirect knowledge of Mathematical concepts. In this article, we are going to discuss the approach we should follow while solving Data Sufficiency questions. Questions on Data Sufficiency are generally asked in the data interpretation section. Let us learn the concept and approach for solving Data Sufficiency questions. Number properties, factors. The given question is a data sufficiency question in number properties and tests concepts in number of factors of a number and properties of odd and even integers.

This data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in a leap year or the meaning of the word counterclockwise), you must indicate whether - Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

Numbers All numbers used are real numbers. Figures Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight Note. Change of Base Formula or Rule - ChiliMath. I have discussed most of the log rules in a separate lesson.

However, I have intentionally left one out to discuss it here in detail. The log rule is called the Change-of-Base Formula. 4.6: Exponential and Logarithmic Models - Mathematics LibreTexts. While we have explored some basic applications of exponential and logarithmic functions, in this section we explore some important applications in more depth.

Radioactive Decay In an earlier section, we discussed radioactive decay – the idea that radioactive isotopes change over time. One of the common terms associated with radioactive decay is half-life. Exponential Growth and Decay. Exponential growth can be amazing!

The idea: something always grows in relation to its current value, such as always doubling. Example: If a population of rabbits doubles every month, we would have 2, then 4, then 8, 16, 32, 64, 128, 256, etc! Amazing Tree Let us say we have this special tree. It grows exponentially , following this formula: e is Euler's number, about 2.718 At 1 year old it is: e1 = 2.7 mm high ... really tiny! No tree could ever grow that tall. Growth and Decay But sometimes things can grow (or the opposite: decay) exponentially, at least for a while.

Bookshelves - Mathematics LibreTexts. The Bookshelves area in this LibreTexts Library holds texts that are curated by the LibreTexts Development team and can be used either directly or as content for building customized remixes (i.e., texts that are generated from existing content often with customized editing and/or content interspersed) for use in campus Course Shells.

There are two classes of texts found in the Bookshelves: "Textbooks" and "Textmaps". Textbooks are the central spot for integrated content into our library and are identified by "Book:" in their titles. Textmaps are specialized remixes that are constructed to follow the organization of existing commercial textbooks. Textmaps facilitate adoption by faculty that are unable to switch from a commercial textbook to an OER alternative; these texts are identified by "Map:" in their titles. For details on how to have a text added to the bookshelves or how to remix content into your customized remix contact us at info@libretexts.org. 4.6: Exponential and Logarithmic Models - Mathematics LibreTexts. Geometry.

It’s the Law Too — the Laws of Logarithms. Copyright © 2002–2019 by Stan Brown Summary: Do you have trouble remembering the laws of logarithms? Do you know why you can change log(x)+log(y) to a different form, but not log(x+y)?