Question 178445
Studies have shown that the population of rats inside an average sized house grows exponentially depending upon the number of cats that can be found on the premises. A a function of time the population of rats is approximated by the equation: 
p(t)=P(K/C)^t 
Where K=4.2 is a constant derived from experiment P is the initial popuation of rats, C is the number of cats, and t is given in weeks. 
How many cats are necessary to stop the number of rats from increasing? Explain.
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p(t)=P(K/C)^t
p(t) = P(4.2)/C)^t
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Since t is always increasing p(t) will = 4.2P when C = 4.2 cats.
and p(t) will decrease if C is greater than 4.2 cats because the
fraction K/C will be greater than zero but less than one; that will
make p(t) a decreasing function..
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Cheers,
Stan H.