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?

Question

2675 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-14T10:57:47

Population= 5,657

This is a Geometric progression with terms:

$T_{1}, T_{2}, T_{3} T_{4}$ $T_1," " T_2," " T_3" " T_4$
$1,000, 2,000, 4,000, 8,000 ....,$
$"0 hrs, 12 hrs, 24 hrs 36hrs.$

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.