A colony of ants has 50,000 members. Sione thinks the colony will grow at a rate of 3.1% each hour. How many ants should he expect there to be in the colony after 10 hours? Express your answer rounded to the nearest whole number.
Mathematics · High School · Thu Jan 21 2021
Answered on
Given:
Colony of ants = 50,000
growth rate = 3.1% or 0.031
Determine the number of ants after 10 hours.
The formula for population growth can be written as,
Future Colony Number = Present Colony ( 1 + rate)^number of hours
Solution:
Substitute the given values to the future colony formula.
Future Colony = 50,000 ( 1 + 0.031)^10
Future Colony = 50,000 ( 1.031)^10
Future Colony = 67,851.1 or 67,851
Final answer:
The expected number of ants after 10 hours is 67,851.