SOLUTION: The population of the United States in 1994 was about 260 million, and the population was about 277 million in 2003. Find the growth rate in the United States and write an expon

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: The population of the United States in 1994 was about 260 million, and the population was about 277 million in 2003. Find the growth rate in the United States and write an expon      Log On


   

Question 83895: The population of the United States in 1994 was about 260 million, and the population was about 277 million in 2003.
Find the growth rate in the United States and write an exponential function describing this situation.
What was the projected percent of increase annually?
The population was/will be 1 billion in what year?
Answer by stanbon(75887) About Me  (Show Source):
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The population of the United States in 1994 was about 260 million, and the population was about 277 million in 2003.
Find the growth rate in the United States and write an exponential function describing this situation.
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growth rate = [one year change in population]/260 = [277-260]/9/260 = 17/9/260=1.8888/260=0.007
EQUATION:
P(t) = 260(1.007)^t ( in millions)
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What was the projected percent of increase annually?
% increase = [one year increase/last year total] = 1.88888/260 = 0.007 or 0.7%
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The population was/will be 1 billion in what year?
Comment: 1000 million = 1 billion
Let P(t) = 1000; find "t":
1000 = 260 (1.007)^t
Divide both sides by 260 to get:
3.84615.. = (1.007)^t
Take the log of both sides:
tlog(1.007) = log3.84615
t = [log3.84615]/[log(1.007)]
t = 193.11 years
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1994 + 193 = 2187
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Cheers,
Stan H.