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#