Question 691562: The population of a certain city was 116,000 in 1995, and the observed relative growth rate is 4% per year.
a) Find a function that models the population after t years.
n(t)=_______
b) Find the projected population in the year 2004. Round the answer to the nearest thousand.
c) In what year will the population reach 200,000?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The population of a certain city was 116,000 in 1995, and the observed relative growth rate is 4% per year.
a) Find a function that models the population after t years.
n(t)=116,000(1.04)^t
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b) Find the projected population in the year 2004. Round the answer to the nearest thousand.
n(9) = 116,000(1.04)^9 = 165,104
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c) In what year will the population reach 200,000?
Solve:
200,000 = 116,000*1.04^t
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1.04^t = 1.7241
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Take the log of both sides:
t*log1.04 = log1.7241
t = log(1.7241)/log(1.04)
t = 13.88 = 14 years when rounded up
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Ans: 1995 + 14 = 2009 (Year the population will be 200,000)
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