Math: Small World Isn't It Project Portfolio
The Small World Isn't It Project Portfolio is a collection of assignments that focused on developing a fomula for exponential growth. The goal of this project is to find a formula that could be used to solve the problem of how many years it would take in order for the world's population to reach the point where everyone is "squashed" within inches of each other. This problem uses many different mathematical ideas such as a Standard Base and Natural Logs.
A Derivative is the rate of change in a function due to one of its variables. In order to find the derivative in a function, you would use the equation Δy/Δx, or delta y over delta x.
The Standard Base is the number 2.71828 and is represented by the symbol e. This number is the base constant for hundreds of mathematic calculations and formulas.
Logarithms are the power (or exponent) to which a certain number (the base) is raised to produce a given number. A Natural Log is a type of logarithm that is used to solve for numbers or equations with a base of e (2.71828), also known as the Standard Base.
Before solving for the main problem, we were taught many different formulas and problems to get us used to solving exponental growth formulas. Our first assignment used a simple formula, which is y = 2^x, to find exponental growth over a short period of time. For this problem, we were required to graph this problem in order to show the amount of growth. The next assignment introduced us into a new mathematical idea called logarithms. This assignment taught us that logarithms are a different way to write out an exponential formula and how to convert an exponential form to logarithmic form. Several other assignments focused on practicing how to find derivatives in exponential growth formulas using the formula
The equation used for solving the main problem is y = k * e ^ (c * x). In this equation y is the answer. This is the amount of years that it would take for the human population of the world to take up every inch of available space. k and c are variables that can be changed or solved for. x is a constant in the equation that represents the human population needed in order for the world to be "squashed". This constant was solved for in class as 1.6 * 10 ^ 15 people. e symbolized the standard base.
A Derivative is the rate of change in a function due to one of its variables. In order to find the derivative in a function, you would use the equation Δy/Δx, or delta y over delta x.
The Standard Base is the number 2.71828 and is represented by the symbol e. This number is the base constant for hundreds of mathematic calculations and formulas.
Logarithms are the power (or exponent) to which a certain number (the base) is raised to produce a given number. A Natural Log is a type of logarithm that is used to solve for numbers or equations with a base of e (2.71828), also known as the Standard Base.
Before solving for the main problem, we were taught many different formulas and problems to get us used to solving exponental growth formulas. Our first assignment used a simple formula, which is y = 2^x, to find exponental growth over a short period of time. For this problem, we were required to graph this problem in order to show the amount of growth. The next assignment introduced us into a new mathematical idea called logarithms. This assignment taught us that logarithms are a different way to write out an exponential formula and how to convert an exponential form to logarithmic form. Several other assignments focused on practicing how to find derivatives in exponential growth formulas using the formula
The equation used for solving the main problem is y = k * e ^ (c * x). In this equation y is the answer. This is the amount of years that it would take for the human population of the world to take up every inch of available space. k and c are variables that can be changed or solved for. x is a constant in the equation that represents the human population needed in order for the world to be "squashed". This constant was solved for in class as 1.6 * 10 ^ 15 people. e symbolized the standard base.