Radiocarbon dating differential equation

For a particular situation that we might wish to investigate, our first task is to write an equation (or equations) that best describes the phenomenon.Suppose that we wish to study how a population \(P(t)\) grows with time \(t\text\) We might make the assumption that a constant fraction of population is having offspring at any particular time.In addition, the theory of the subject has broad and important implications.¶We begin our study of ordinary differential equations by modeling some real world phenomena.

For example, we might add a dashpot, a mechanical device that resists motion, to our system.

If we pull or push on the mass and release it, then the mass will oscillate back and forth across the table.

We can construct a differential equation that models our oscillating mass.

The number of trout will be limited by the available resources such as food supply as well as by spawning habitat.

A small population of fish might grow exponentially if the pond is large and food is abundant, but the growth rate will decline as the population increases and the availability of resources declines.

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