The unrestricted growth of bacteria is an example of exponential population growth. Bank accounts that accrue interest represent another example of exponential growth. The mathematical model of exponential growth is used to describe real-world situations in population biology, finance and other fiel
Exponential notation simplifies calculation, especially calculation with very small or large numbers, by using positive and negative numbers to write multiples and submultiples of 10. All numbers can be written as a multiple of 10.
Populations grow exponentially when they can maintain a constant growth rate percentage and can leverage the steady increase in population. Exponential growth of various species have been seen throughout Earth's history.
Transformations of exponential functions occur when the function changes to shift the graph to the left, right, up, down or in reverse. An exponential function can be reversed by adding a negative sign in front of the exponent.
A linear function is graphed as a straight line and contains one independent variable and one dependent variable, whereas an exponential function has a rapid increase or decrease along a curved line in a graph. Linear functions, or equations, take the form "y = a + bx," in which "x" is the dependent
The pre-exponential factor, or frequency factor, is an aspect of the Arrhenius equation and is related to collision theory. The value for this factor varies depending on the chemical reaction and is determined through experimental observation. However, if values of the rate constant, k, are known at
Graphs are beneficial because they summarize and display information in a manner that is easy for most people to comprehend. Graphs are used in many academic disciplines, including math, hard sciences and social sciences. They make appearances in corporate settings, serving as useful tools to convey
The inverse of an exponential function is a logarithm function. An exponential function written as f(x) = 4^x is read as "four to the x power." Its inverse logarithm function is written as f^-1(y) = log4y and read as "logarithm y to the base four."
Converting logarithms to exponential form is a matter of knowing which symbols represent which part of the equation and directly substituting. This conversion can be done in under a minute, and a calculator is only useful if you want to check your answer.
Find the slope of the line (m), and the place where the line crosses the y-axis, known as the y-intercept (b), to write the equation in slope-intercept form, y = mx + b. Use the equation to find the y value for any x on that line.