SOLUTION: 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 o

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.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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.
-----------------
p(t)=P(K/C)^t
p(t) = P(4.2)/C)^t
--------------------------
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..
=========================================
Cheers,
Stan H.
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