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A word for a constant rate of change?
In mathematics, a constant rate of change is called a slope. For linear functions, the slope would describe the curve of the function. The world "constant" in this context means the slope and therefore angle of the curve will not change.
How does the graph of an exponential function differ from the graph of a linear function and how is the rate of change different?
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.
Does a spiral staircase have a constant slope?
Previous answer: "No because the line is not straight and the points of the slop is in different ares." The above is ambiguous. You need to define the term slope. The slope of a helix (or any curve) is normally defined as the slope of a line that is tangent to the helix (curve). And then you need to define, slope with respect to what? Normally that would be slope with respect to a horizontal plane. That slope, by definition, is constant for a helix with a vertical axis. The value of the slope of such a helix is pitch / (2*pi*R), where R is the radius from the axis. Then you have to consider where on the staircase you are. A staircase is not a single helix. It has width, or different radii. If you are walking up stairs at a constant radius R from the axis (on a helix), then the slope is constant. In any case, the average slope of the stairs varies with the radius R on which you are walking, so that would not be a constant.
What does a constant slope mean?
It means that the rise divided by the run for a curve has the same value. If A and B are any two points on the curve, with coordinates (Xa, Ya) and (Xb, Yb), then (Yb - Ya)/(Xb - Xa) is a constant.
How the slope of a curved line at a point can be found?
The slope of a curved line at a point is the slope of the tangent to the curve at that point. If you know the equation of the curve and the curve is well behaved, you can find the derivative of the equation of the curve. The value of the derivative, at the point in question, is the slope of the curved line at that point.
