SOLUTION: The popluation of Oregon grew from 2.8 million in 1980 to 3.42 million in 1990. Write a base-e exponential function to show how popluation depends on time. What population would be

Question 685199: The popluation of Oregon grew from 2.8 million in 1980 to 3.42 million in 1990. Write a base-e exponential function to show how popluation depends on time. What population would be predicted for 2008? After how many years will Oregon's popluation double?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The popluation of Oregon grew from 2.8 million in 1980 to 3.42 million in 1990. Write a base-e exponential function to show how population depends on time.
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y = ae^(rt)
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Using (0,2.8)
2.8 = ae^0
a = 2.8
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Using (10,3.42)
3.42 = 2.8e^(10r)
e^(10r) = 1.22
10r = ln(1.22)
r = 0.0199
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Equation:
y = 2.8e^(0.0199t)
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What population would be predicted for 2008?
f(8) = 2.8*e^(0.0199*8) = 3.28 million
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After how many years will Oregon's population double?
It doubles when e^(0.0199t) = 2
0.0199t = ln(2)
t = ln(2)/0.0199
t = 34.8 years
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Cheers,
Stan H.
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