This task provides a real world context for interpreting and solving exponential equations. There are two solutions provided for part (a). The first solution demonstrates how to deduce the conclusion by thinking in terms of the functions and their rates of change. The second approach illustrates a rigorous algebraic demonstration that the two populations can never be equal.

The purpose of this task is to study an example of a function which varies discretely over time. Step functions are often good examples for this type of function. In practice, instead of a step function, bar graphs are sometimes used. Alternatively, Jessie's method of ''smoothing'' over the jumps is also very common.

This task could be put to good use in an instructional sequence designed to develop knowledge related to students' understanding of linear functions in contexts. Though students could work independently on the task, collaboration with peers is more likely to result in the exploration of a range of interpretations.

This task involves a fairly straightforward decaying exponential. Filling out the table and developing the general formula is complicated only by the need to work with a fraction that requires decisions about rounding and precision.

This task describes two linear functions using two different representations. To draw conclusions about the quantities, students have to find a common way of describing them. We have presented three solutions (1) Finding equations for both functions. (2) Using tables of values. (3) Using graphs.

The purpose of this task is for students to interpret two distance-time graphs in terms of the context of a bicycle race. There are two major mathematical aspects to this: interpreting what a particular point on the graph means in terms of the context, and understanding that the "steepness" of the graph tells us something about how fast the bicyclists are moving.

This book will initiate you into an esoteric world. You will learn and apply the methods of thought that mathematicians use to verify theorems, explore mathematical truth and create new mathematical theories. This will prepare you for advanced mathematics courses, for you will be better able to understand proofs, write your own proofs and think critically and inquisitively about mathematics.

This task provides an exploration of a quadratic equation by descriptive, numerical, graphical, and algebraic techniques. Based on its real-world applicability, teachers could use the task as a way to introduce and motivate algebraic techniques like completing the square, en route to a derivation of the quadratic formula.

This task is for instructional purposes only and builds on ``Building an explicit quadratic function.''

This is the first of a series of task aiming at understanding the quadratic formula in a geometric way in terms of the graph of a quadratic function.

This task is intended for instruction and to motivate "Building a general quadratic function.''

This course provides an introduction to applied concepts in Calculus that are relevant to the managerial, life, and social sciences. Students should have a firm grasp of the concept of functions to succeed in this course. Topics covered include derivatives of basic functions and how they can be used to optimize quantities such as profit and revenues, as well as integrals of basic functions and how they can be used to describe the total change in a quantity over time.

Full course of Algebra 1 is presented online by Georgia Virtual Learning. Audio, video, text, games and activities are included to engage ninth grade students in learning.

The student will learn the mechanics of editing and compiling a simple program written in C++ beginning with a discussion of the essential elements of C++ programming: variables, loops, expressions, functions, and string class. Next, the student will cover the basics of object-oriented programming: classes, inheritance, templates, exceptions, and file manipulation. The student will then review function and class templates and the classes that perform output and input of characters to/from files. This course will also cover the topics of namespaces, exception handling, and preprocessor directives. In the last part of the course, the student will learn some slightly more sophisticated programming techniques that deal with data structures such as linked lists and binary trees. Upon successful completion of this course, students will be able to: Compile and execute code written in C++ language; Work with the elementary data types and conditional and iteration structures; Define and use functions, pointers, arrays, struct, unions, and enumerations; Write C++ using principles of object-oriented programming; Write templates and manipulate the files; Code and use namespaces, exceptions, and preprocessor instructions; Write a code that represents linked lists and binary trees; Translate simple word problems into C++ language. (Computer Science 107)

One of the most magnificent structures in the computer science world is the function. Functions (sometimes called procedures) are mini programs that you can use over and over inside of your bigger program. This lesson will help students intuitively understand why combining chunks of code into functions can be such a helpful practice.

Students will begin to understand how functions can be helpful in this fun and interactive Minecraft adventure!

Students have practiced creating impressive designs in Artist and navigating mazes in Bee, but today they will use functions to harvest crops in Harvester. This lesson will push students to use functions in the new ways by combining them with `while` loops and `if / else` statements.

Students will be introduced to using functions with the Artist. Magnificent images will be created and modified. For more complicated patterns, students will learn about nesting functions by calling one function from inside another.

Students will begin to understand how functions can be helpful in this fun and interactive Minecraft adventure!

Students have practiced creating impressive designs in Artist and navigating mazes in Bee, but today they will use functions to harvest crops in Harvester. This lesson will push students to use functions in the new ways by combining them with `while` loops and `if / else` statements.