Under natural circumstances the population of mice on a certain island would inc

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?

Answer is 94,742 please show step by step

Explanation / Answer

mice grew from P = 50,000 to A = 100,000 in n = 10 years using compound interest formula A = P(1+(R/100)^n put all values, rate of growth = 7.177 %p.a = 0.598% per month in 1st month at 0.598% mice population grows to 100,000(1+0.00598) = 100,598 out of which 1000 are killed so mice left at end of 1st month = 100,598-1000 = 99958 at starting of second month mice population = 99958 which grow to 100196 mice again 1000 are killed so mice left at end of 2nd month is 99196 continue this trend to get your answer which is approx equal to 94720

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