Many population systems are growing exponentially. The mathematical model of the exponential growth of the system is
[tex]y' = ky_{o} e^{kt} = ky[/tex]
Where
[tex]y_{o}[/tex] = initial state of the system
[tex]k[/tex] > 0 positive constant or growth constant
This equation needs derivatives and is called a differential equation. Notice that population growth is proportional to the current function value, which is a key to exponential growth.
One common example of differential growth is population growth. In this instance is the bacteria population. As mentioned before, population growth is proportional to the current function value (K), which means the more bacteria reproduce then the faster population growth.
In the following figure, we can see after only 120 minutes, an initial population of 200 bacteria with a growth constant of 0.02 would be 10 times its outset quantity.
Know more about exponential growth here: https://brainly.com/question/11487261
The question was incomplete. This is a general answer.
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