A certain population of bacteria which demonstrates exponential growth doubles in size every 12 hours. If the initial population is 1,000 bacteria, what will be the population after 30 hours?

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Answer 1 · 2016-07-14T10:57:47

Population= 5,657

This is a Geometric progression with terms:

#T_1," " T_2," " T_3" " T_4 #
#1,000, 2,000, 4,000, 8,000 ....,#
#"0 hrs, 12 hrs, 24 hrs 36hrs.#

The first term, 'a' is 1,000.
The common ratio 'r' is 2.

The general term #T_n = ar^(n-1)#

The population after 30 hours, will be between the Third and 4th terms. #30/12 = 2.5#

Population =# 1000 xx 2^2.5 = 5,656.85#

However, we can't have 0.8 of a bacteria, so we would round to the nearest whole number.
Population= 5,657.