SOLUTION: I have a word problem, the textbook question is "There are 5400 ants in a colony. If there were 1200 ants in the colony 8 months ago, what is the monthly rate of growth?" I thin

Question 301540: I have a word problem, the textbook question is "There are 5400 ants in a colony. If there were 1200 ants in the colony 8 months ago, what is the monthly rate of growth?"
I think the equation is written as but I'm not sure. Either way, I still can't figure out how to solve it. Any help would be much appreciated!!
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
"There are 5400 ants in a colony. If there were 1200 ants in the colony 8 months ago, what is the monthly rate of growth?"
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If the number increases linearly, it's (5400 - 1200)/8 = 525/month
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It's more likely to be an exponential increase, tho, with a constant growth.
5400 = 1200*e^rt (t in months)
e^(8r) = 5400/1200 = 4.5
8r = ln(4.5)
r = ln(4.5)/8 =~ 0.188
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If it's done on a monthly basis:
5400 = 1200(1 + r)^8
(1+r)^8 = 4.5
1+r = 4.5^(1/8)
r = 4.5^(1/8) - 1
r =~ 0.206845

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