Question

The Museum of Science in Boston displays a running total of the U.S population. On May 11,1993, the total was increasing at the rate of 1 person every 14 sec. The displayed population figure for 3:45 P.M. that day was 257,313,431.
a) Assuming exponential growth at a constant rate, find the rate constant for the population's growth (people per 365 day year).
b) At this rate, what will the U.S population be at 3:45P.M. Boston time on May 11, 2008?

Answer 1

a) to find the amount of population increase from 1993 to 1994:
- calculate how many seconds are in one year (365 days * 24 hours/day * 60 minutes/hour * 60 seconds/minute)

because the population increased by 1 person every 14 seconds, divide the previous # by 14 to get the population growth in one year

from there, divide population growth in one year / original population in May 1993 to get the growth constant

b) between May 11,1993 and May 11, 2008 at 3:45, exactly 15 years have passed. therefore you can use the equation

P(x) = P0 * (1 + r)^t

plugging in the original population as P0, the rate constant as r, and 15 as t, to calculate the new population P(x)