A colony of bacteria grows by 10% per hour. By what percent will the colony grow after five hours?

1 Answer
Dec 8, 2016

The colony will have grown by color(green)(61.051%) after 5 hours.

Explanation:

If p_t is the population of a colony after t time units and r is the growth factor per time unit:
color(white)("XXX")p_t=p_0(1+r)^t

For the given values
color(white)("XXX")p_5=p_0(1+0.10)^5
color(white)("XXXX") = 1.1^5p_0
color(white)("XXXX")= 1.61051p_0 (calculator used here)
color(white)("XXXX")=p_0+0.61051p_0

0.61051=61.051%