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(75887)   (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.
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a) Which town is growing faster?
Initially its Happyville.
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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
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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+
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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.
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