Cramped Quarters Island Is a Tiny Island Which, Although Able $Q(t)$

question 42

Essay

Cramped Quarters Island is a tiny island which, although able to support a limited population of rabbits, doesn't have enough space or food supplies to support unlimited exponential growth.It is suggested that if Q(t)= population of rabbits on Cramped Quarters Island at time t, then the quantity (800 - Q(t))will be an exponentially decaying function of t.If at time t = 0 there were 250 rabbits, and the population was increasing at an instantaneous rate of 100 rabbits per year, give the general formula for $Q(t)$
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Definitions:

Independent Variable

A factor manipulated by the experimenter to investigate its effects on the dependent variable in a study.

Factorial Design

A design in which all levels of each independent variable are combined with all levels of the other independent variables. A factorial design allows investigation of the separate main effects and interactions of two or more independent variables.

Main Effect

The direct effect of an independent variable on a dependent variable.

Factorial Design

An experimental design approach that involves investigating the effects of two or more independent variables at multiple levels on a dependent variable.