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What kind of graphs does exponential growth makes?
A curve
What is the letter used to refer to the characteristics shape of an exponential growth curve?
J
Why is Moore's law line a straight graph?
Moore's Law states essentially the exponential nature of the curve existing between transistor count in a single chip and passed time in years. Although in most websites and sources, the curve shown is straight with transistor # being in the Y axis, it must be observed, Moore stated that the curve is exponential. Thus the graphs, if linear are logarithmic curves, as a log graph for an exponential curve is linear in nature. So instead of transistor nos (x) , we use ln(x)
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.
Would the graph of an exponential decay function would have a curve upward along the x-axis towards negative infinity?
No, it would not.
An exponential growth function represents a quantity that has a constant halving time?
That would be an exponential decay curve or negative growth curve.
What kind of graphs does exponential growth makes?
A curve
Why do the points of a geometric sequence lie on an exponential curve only when the common ratio is positive?
If the common ratio is negative then the points are alternately positive and negative. While their absolute values will lie on an exponential curve, an oscillating sequence will not lie on such a curve,
What is a j-shaped curve called?
A J-shaped curve is often referred to as exponential growth, which illustrates a rapid increase in a population or entity over time. This curve demonstrates a steady rise and acceleration in growth without any limiting factors in place.
Why does exponential growth show a characteristic j-shaped curve?
Unlimited resources
What is the letter used to refer to the characteristics shape of an exponential growth curve?
J
What is an Allen curve?
An Allen curve is a graphical representation which reveals the exponential drop in frequency of communication between engineers as the distance between them increases.
What does exponential growth curve represent?
An exponential growth curve represents a pattern of growth where the rate of growth is proportional to the current size of the population or system. This leads to rapid and continuous acceleration in growth over time. Examples include bacterial growth in a petri dish or compound interest in finance.
Why is Moore's law line a straight graph?
Moore's Law states essentially the exponential nature of the curve existing between transistor count in a single chip and passed time in years. Although in most websites and sources, the curve shown is straight with transistor # being in the Y axis, it must be observed, Moore stated that the curve is exponential. Thus the graphs, if linear are logarithmic curves, as a log graph for an exponential curve is linear in nature. So instead of transistor nos (x) , we use ln(x)
What shape is bounded by a straight line and a curve?
There is no specific name for it since the curve is not specified. The curve could be a conic section (circle, ellipse, parabola, hyperbola), or a trigonometric function, or a polynomial, exponential, etc. Or a combination of these.
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.
Why can two exponential surfaces not cross each other?
Two exponential surfaces cannot cross each other because they are defined by exponential functions, which are always increasing or decreasing but never intersecting. Each point on an exponential surface corresponds to a unique value on the curve, so two exponential surfaces intersecting would imply a contradiction in values.
