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The rodent population in a city is currently estimated at 4000040000. if it is expected to double every 1010 years, when will the population reach 11 million? round to the nearest hundredth of a year.

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wolf1728
40,000 rodents doubles every 10 yearswhen will population = 11,000,000

First, we solve for rate:
Rate = 10^[(log[Ending Amount / Beginning Amount] ÷ time)]  -1for this equation we'll say beginning amt = 40,000 end amt = 80,000
Rate = 10^[log (80,000 / 40,000) / 10 years] -1Rate = 10^ (log(2) / 10) -1Rate = 10^ (0.30102999566 / 10) -1Rate =(10^.030102999566) -1Rate = 1.0717734625 -1
Rate = .0717734625

NOW, we solve for time:Time = log(ending amount / beginning amount) ÷ log (1 + rate)

Time =log(11,000,000 / 40,000) / log(1.0717734625)
Time =log (275) / log(1.0717734625)
Time = 2.4393326938 /  0.030102999552Time = 81.0328781219 Years
Time = 81.03 Years (rounded)
Source 1728.com/expgrwth.htm

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