Cramped Quarters Island Is a Tiny Island Which, Although Able

question 50

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.Given that there were 400 rabbits at time t = 0, and 500 rabbits one year later, find the general formula for Q(t), the population of rabbits on Cramped Quarters Island at time t and use it to determine the rabbit population after 3 years (to the nearest rabbit).

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Definitions:

Photosynthesis

A process by which green plants and some other organisms use sunlight to synthesize foods from carbon dioxide and water. Photosynthesis in plants generally involves the green pigment chlorophyll and generates oxygen as a byproduct.

Equation

A mathematical statement that asserts the equality of two expressions, usually represented by the symbol "=".

Worms

Malicious software programs that replicate themselves in order to spread to other computers, often causing harm by exploiting vulnerabilities.

User Interaction

The process and manner in which users interface and engage with digital products and services.