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manigraja100
Students
 
Posts: 14
Joined: Sun Mar 03, 2013 12:00 am
 

population-word problem

by manigraja100 Sat Jun 29, 2013 2:34 am

An insect colony doubles in population every 10 years. Its population is reduced by 20% every 7 years. After 50 years, the population of this colony is how many times its initial population, rounded to the nearest integer.
How to solve this problem ?
tommywallach
Manhattan Prep Staff
 
Posts: 1917
Joined: Thu Mar 31, 2011 11:18 am
 

Re: population-word problem

by tommywallach Sat Jun 29, 2013 11:35 am

Hey Mani,

An insect colony doubles in population every 10 years. Its population is reduced by 20% every 7 years. After 50 years, the population of this colony is how many times its initial population, rounded to the nearest integer.
How to solve this problem ?

X * 2^5 * .8^7 = X * Y

X = initial population
Y = what the question is asking for

2^5 represents 5 doublings (years 10, 20, 30, 40, 50)
.8^7 represents 7 times taking 80% (years 7, 14, 21, 28, 35, 42, 49)

Voila! (It solves to 7).

-t