it slopes downward. it has a negative slope. it it really high when it is close to zero but gets really low as the x-value goes greater.
Yuo cannot include a graphical illustration here. Take a look at the Wikipedia, under "exponential function" and "logistic function". Basically, the exponential function increases faster and faster over time. The logistics function initially increases similarly to an exponential function, but then eventually flattens out, tending toward a horizontal asymptote.
It is an exponential function.
an exponential function flipped over the line y=x
When the graphdecreasesat a rapid rate. Instead of just a negative straight line it will be a negative half parabola decreasingextremelyfast and then leveling out.
If two variables are inversely related, then a graph showing their relationship should be shaped like a hyperbola. A hyperbola will start out really high, drop a lot in a short distance, then drop less and less as the graph goes further to the right. It looks similar to an exponential decay function, but less extreme. Here is an example of what one could look like: http://www.wolframalpha.com/input/?i=1%2F4x (In most practical applications, only the right side of the graph would be shown.)
Exponential Decay. hope this will help :)
An exponential function is a nonlinear function in the form y=ab^x, where a isn't equal to zero. In a table, consecutive output values have a common ratio. a is the y-intercept of the exponential function and b is the rate of growth/decay.
No, it would not.
The relationship between a logarithmic function and its graph is that the graph of a logarithmic function is the inverse of an exponential function. This means that the logarithmic function "undoes" the exponential function, and the graph of the logarithmic function reflects this inverse relationship.
An exponential graph typically exhibits a J-shaped curve. For exponential growth, the graph rises steeply as the value of the variable increases, while for exponential decay, it falls sharply and approaches zero but never quite reaches it. The key characteristic is that the rate of change accelerates or decelerates rapidly, depending on whether it is growth or decay.
The trend of an exponential graph depends on the base of the exponential function. If the base is greater than one (e.g., (y = a \cdot b^x) with (b > 1)), the graph shows exponential growth, rising steeply as (x) increases. Conversely, if the base is between zero and one (e.g., (y = a \cdot b^x) with (0 < b < 1)), the graph depicts exponential decay, decreasing rapidly as (x) increases. In both cases, the graph approaches the x-axis asymptotically but never touches it.
The graph of a linear function is a line with a constant slope. The graph of an exponential function is a curve with a non-constant slope. The slope of a given curve at a specified point is the derivative evaluated at that point.
An exponential function does not create a linear shape on a graph. Instead, it produces a curve that either rises or falls rapidly, depending on whether the base of the exponent is greater than or less than one. The graph is characterized by its continuous and smooth nature, exhibiting either exponential growth or decay. Additionally, it does not form any circular or parabolic shapes, which are seen in other types of functions.
f(x)=2X-2
As time passes - as the graph goes more and more to the right, usually - the graph will get closer and closer to the horizontal axis.
Yuo cannot include a graphical illustration here. Take a look at the Wikipedia, under "exponential function" and "logistic function". Basically, the exponential function increases faster and faster over time. The logistics function initially increases similarly to an exponential function, but then eventually flattens out, tending toward a horizontal asymptote.
The graph of an exponential function f(x) = bx approaches, but does not cross the x-axis. The x-axis is a horizontal asymptote.