Question 86806: In 2000, the population of Israel was approximately 6.04 million and by 2050 it is projected to grown to 10 million. Use the exponential growth model A = Aoe^kt, in which t is the number of years after 2000, to find an exponential growth function that models the data.
In which year will Israel's population be 9 million?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In 2000, the population of Israel was approximately 6.04 million and by 2050 it is projected to grown to 10 million. Use the exponential growth model A = Aoe^kt, in which t is the number of years after 2000, to find an exponential growth function that models the data.
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You have two points: (0,6.04) and (50,10)
A(t) = Aoe^kt
If t = 50
10 = 6.04e^(10k)
1.656 = e^(10k)
Take the ln of both sides to get:
ln(1.656) = 10k
k = 0.05042
EQUATION is Therefore A(t) = 6.04e^(0.05042t)
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In which year will Israel's population be 9 million?
9 = 6.04e^(0.05042t)
1.49 = e^(0.05042t)
Take the ln of both sides to get:
0.05042t = 0.3988206
t = 7.91 years
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Nine million in the year 2008
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Cheers,
Stan H.
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