# SOLUTION: Happyville and Smileytown both have a population of 10,000 people presently. Hap- pyville is increasing by 1500 people a year and Smileytown is increasing by 15% a year. a) Whic

Algebra ->  Algebra  -> Exponential-and-logarithmic-functions -> SOLUTION: Happyville and Smileytown both have a population of 10,000 people presently. Hap- pyville is increasing by 1500 people a year and Smileytown is increasing by 15% a year. a) Whic      Log On

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 Question 252076: Happyville and Smileytown both have a population of 10,000 people presently. Hap- pyville is increasing by 1500 people a year and Smileytown is increasing by 15% a year. a) Which town is growing faster? b) Find formulas for the populations of these towns as function of time t in years. c) Use part b) to predict the size of both towns 5 years from now. d) Find a year in which population of Happyville will be over 25000. Do the same for Smileytown.Answer by stanbon(57984)   (Show Source): You can put this solution on YOUR website!Happyville and Smileytown both have a population of 10,000 people presently. Hap pyville is increasing by 1500 people a year and Smileytown is increasing by 15% a year. ------ a) Which town is growing faster? Initially its Happyville. ---------------------- b) Find formulas for the populations of these towns as function of time t in years. H(x) = 10,000 + 1500x S(x) = 1000(1.15)^x ---------------------------- c) Use part b) to predict the size of both towns 5 years from now. H(5) = 10,000 + 1500*5 = 17500 S(5) = 10,000(1.15)^5 = 29113+ ------------------------------------ d) Find a year in which population of Happyville will be over 25000. Do the same for Smileytown. Happy: 10000+1500x > 25000 1500x > 15000 x > 10 years ---- Smiley: 10000(1.15)^x > 25000 1.15^x > 5/2 x*log1.15 > log(5/2) x > 6.556 years ---------------------- Cheers, Stan H.