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Why radioactivity is exponential?
The number of atoms that decay in a certain time is proportional to the amount of substance left. This naturally leads to the exponential function. The mathematical explanation - one that requires some basic calculus - is that the only function that is its own derivative (or proportional to its derivative) is the exponential function (or a slight variation of the exponential function).
What problem cannot be represented by a linear function?
Temperature Radio Active decay interest % population % Projectile of a ball exponential decay or growth depreciation %
What is the difference between exponential growth and decay?
Exponential growth is when the amount of something is increasing, and exponential decay is when the amount of something is decreasing.
What is the difference exponential growth and decay?
They are incredibly different acceleration patterns. Exponential growth is unbounded, whereas exponential decay is bounded so as to form a "dynamic equilibrium." This is why exponential decay is so typical of natural processes. To see work I have done in explaining exponential decay, go to the page included in the related links.
When would you use a power function and when would you use a exponential function?
Both of these functions are found to represent physical events in nature. A common form of the power function would be the parabola (power of 2). One example would be calculating distance traveled of an object with constant acceleration. d = V0*t + (a/2)*t². The exponential function describes many things, such as exponential decay: like the voltage change in a capacitor & radioactive element decay. Also exponential growth (such as compound interest growth).
Does Exponential decay occurs if the base of an exponential function is a positive integer?
Yes.
How does radioactive decay relate to precalculus?
it is a natural example of the exponential function
In a medical experiment the number of bacteria is halved every hour. What type of function represents this pattern?
Exponential Decay - Apex
What exponential decay function describes an amount that decreases exponentially over time.?
True
Why radioactivity is exponential?
The number of atoms that decay in a certain time is proportional to the amount of substance left. This naturally leads to the exponential function. The mathematical explanation - one that requires some basic calculus - is that the only function that is its own derivative (or proportional to its derivative) is the exponential function (or a slight variation of the exponential function).
What are some characteristics of the graph of an exponential function?
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.
Tha half life of an atom is 50 years what is a possible exponential function for this decay?
sf
Which term describes a function in which there is a common difference between each y-value?
exponential decay
Is an exponential decay function represent a quantity that has a constant halving time?
A quantity is said to be subject to exponential decay if it decreases at a rate proportional to its value. The time required for the decaying quantity to fall to one half of its initial value.Radioactive decay is a good example where the half life is constant over the entire decay time.In non-exponential decay, half life is not constant.
An exponential growth function represents a quantity that has a constant halving time?
That would be an exponential decay curve or negative growth curve.
An exponential decay function represents a quantity that has a decreasing halving time?
exponential decay doesnt have to have a decreasing halving time. it just decays at a certain percentage every time, which might be 50% or might not
Who invented exponentail growth and exponential decay?
Reverend Thomas Malthus developed the concept of Exponential Growth (another name for this is Malthusian growth model.) However the mathematical Exponent function was already know, but not applied to population growth and growth constraints. Exponential Decay is a natural extension of Exponential Growth
