Exponential Growth, its properties, how graph relates to the equation and formula-Visual Lesson, Mat

Exponential Growth Equations and Graphs. Formula and graph for exponential growth equations.

Properties. Property #1) rate of growth starts slow and increases ( Read on, to learn more about this property, which is the primary focus of this web page) Property #2) The domain is Answer. Of note: Exponential decay is not the inverse of exponential growth. How Equation relates to Graph. The graph's asymptote at x -axis. What about when b is exactly equal to 1 ? Answer.

As you can see from the work above, and the graph, when b is 1, you end up with the equation of a horizontal line ( Link ) . The Graph. Property #1) Rate of growth of exponential growth increases more and more, until it becomes massive! Table of Values. The table of values for the exponential growth equation $$y = 9^x $$ demonstrates the same property-growth rate starts slow and soon gets massive. Just look at the difference between x = 7 and x = 8, the value of the function increases by more than 38 MILLION! How does this compare to other graphs/functions? As the graph below shows, exponential growth. at first , has a lower rate of growth than the linear equation f(x) =50x at first , has a slower rate of growth than a cubic function like f(x) = x 3 , but eventually the growth rate of an exponential function f(x) = 2 x , increases more and more -- until the exponential growth function has the greatest value and rate of growth ! Moral of the story: Exponential growth eventually grows at massive rates, even though it starts out growing slowly. This 'trend' is true and , when compared to other graphs, exponential growth eventually outpaces most other functions's rate of increase.