SOLUTION: The population of a country is growing exponentially. The population in millions was 110 in 1970 and 140 in 1980. (a) What is the population t years after 1970? (b) How long

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Question 268632: The population of a country is growing exponentially. The population in millions was 110 in 1970 and 140 in 1980.
(a) What is the population t years after 1970?
(b) How long does it take the population to double?
(c) When will the population be 400 million?
I know I need to use logs...but I can't seem to get it completely right. Any help would be much appreciated!!
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
The population of a country is growing exponentially. The population in millions was 110 in 1970 and 140 in 1980.
N(t) = ab^t
Determine a and b
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Let 1970 be represented by "0"
110 = ab^0
So a = 110
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140 = ab^10
140 = 110b^10
b^10 = 14/11
b = 1.0244
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Equation:
N(t) = 110(1.0244)^t

(a) What is the population t years after 1970?
N(t) = 110(1.0244)^t
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(b) How long does it take the population to double?
220 = 110(1.0244)^t
1.0244^t = 2
Take the log of both sides and solve for "t":
t = log(2)/log(1.0244)
t = 28.75 years
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(c) When will the population be 400 million?
110(1.0244)^t = 400
1.0244^t = 3.64
Solve for "t" by using logs.
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Cheers,
Stan H.