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When the town of Manning first started its voluntary recycling program, 2500 of the town’s residence participated. The town predicts that the number of people participating in the recycling program will increase by 5% each year.

Which explicit rule can be used to determine the number of people participating in the program in the fifth year?

A. an=2500(1.05)n

B. an=2500(0.05)n

C. an=2500(1.05)n−1

D. an=2500(0.05)n−1

I have trouble understanding these so if you could explain how you did it that would be much appreciated.

Dec 14, 2018

#1
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Note : Here....I'm assuming that "in the fifth year" means "after five years"

an =  Final number

2500 = Starting number

Growth rate (express as a decimal ) =  5%   =  .05

n = number of years

So....we have

Final number =  Starting number ( 1 + growth rate)^n

an  =  2500 (1 + .05)^n        (simplify)

an = 2500 (1.05)^n

Dec 14, 2018
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Okay thanks you for showing me how you did it. It helped me understand the problem better.

awsometrunt14  Dec 14, 2018
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CPhill  Dec 14, 2018
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I tried that answer and I got it inccorect. Could you explain how it was wrong?

awsometrunt14  Dec 14, 2018
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OK....I see what they are assuming...

They are assuming that  during  the 1st year, we have 2500

So...."in the 5th year"  means  "after 4 years"

So....in that case

2500 (1.05)^(n - 1)   is correct.... !!!

CPhill  Dec 14, 2018
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Oh okay thank you!!

awsometrunt14  Dec 14, 2018