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Let P(t) be the number of rabbits living in a national park in month t . What does the expression P(t + 1) represent?

A. P(t) represents the initial rabbit population, and P(t + 1) represents the population after one month.
B. P(t + 1) represents the rabbit population in the (t + 1) -th month.
C. P(t + 1) represents the average rabbit population over t months.
D. P(t + 1) represents the difference in rabbit population between month t and month t + 1 .

User Chenglong
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1 Answer

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The expression P(t + 1) represents the number of rabbits living in a national park one month after month t, which is essentially the rabbit population in the (t + 1)-th month.

The expression P(t + 1) represents the number of rabbits living in a national park in the month following month t. Specifically, if t is the current month, then t + 1 is the next month. Answer choice B correctly defines P(t + 1) as representing the rabbit population in the (t + 1)th month.

This is in line with conventional notation in population dynamics where P(t) signifies the population at time t. Therefore, P(t + 1) shifts the focus by one time unit, providing the population count for the subsequent month.

It is important to note that P(t + 1) is not the initial population, the average population, or the difference in population, but simply the population at a later time.

Understanding this notation is crucial when working with models of population growth like the exponential model P = Poer(t-to) or in assessing the carrying capacity of an ecosystem, represented as Q in ecological equations.

User Rez Moss
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