Under natural circumstances the population of mice on a certain island would inc
ID: 1947694 • Letter: U
Question
Under natural circumstances the population of mice on a certain island would increase at a rate proportional to the number of mice present at any time, provided the island had no cats. There were no cats on the island from the beginning of 1970 to the beginning of 1980, and during this time the mouse population doubled, reaching an all-time high of 100,000 at the beginning of 1980. At this time the people of the island importedA number of cats to kill the mice. If the indicated natural rate of increase of mice was thereafter offset by the work of the cats, who killed 1000 mice a month, how many mice remained at the beginning of 1981?Explanation / Answer
dN/dt = k N
N = No e^(kt)
(10 y ) = 2 No = No e^(k10)
k = ln(2) / 10
= No e^(ln 2 * (t/10)) = No 2^(t/10)
dN/dt = (ln (2)/10) N
(11 y) = 100 000 - 1000 * 12 = 84 000
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