The U.S. Census Bureau keeps a running clock totaling the U.S. population. On Ma

Question

The U.S. Census Bureau keeps a running clock totaling the U.S. population. On March 28, 2008, the total was increasing at a rate of 1 person every 1212 seconds. The population figure for 2:21 P.M. EST on that day was 303,714,725.303,714,725.
1. Find the instantaneous rate of change for the population's growth at time 2:21 P.M. EST, March 28, 2008(people per 365-day year)

2. Assuming exponential growth at a constant growth rate k, what will the U.S. population be at 2:21 P.M. EST on March 28, 2015?

Explanation / Answer

The instantaneous population's growth at time 2:21 P.M. EST, March 28, 2008 was 1 per 1212 second or 1/1212 per second or, (1/1212) *60*60*24*365 = 26019.8 or 26020 ( on rounding off to the nearest whole number) people per year ( 1 year = 365 days = 365*24 hours = 365*24*60 minutes = 365*24*60*60 seconds). Since the present US population is 303,714,725, the rate of growth is 26020/303,714,725= 0.00008567250073 The exponential formula for population growth is A = Pekt where P and A are the present population and population after t years respectively and k is the rate of growth. Here, P = 303,714,725.303,714,725, k = 26020 and t =7. Hence, the U.S. population at 2:21 P.M. EST on March 28, 2015 will be 303,714,725 e0.00008567250073*7 = 303,714,725 e0.000599707505 = 303,714,725 *1.00059989 = 303, 896,920 (on rounding off to the nearest whole number).

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