Question 205515
In 2000, the population of Isreal was approximeatly 6.04 million and the population of the Palestinians in the West Bank, Gaza Strip, and East Jerusalem was approximately 3.2 million in 2050 Israel is projected to grow to 10 million and the population of Palestinians to 12 million. 
Use the exponential growth mdoel A=A(subscript, 0)e^kt, in which t is the number of years after 2000 to find an exponential growth function that models the data for the Israeilis and growth function that models the data for the Palestinians. n which year will each of the populations reach 9 million?? 
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A(t) = Ao*e^kt
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You have two points for each of the peoples.
Israelis: (0,6.04), (50,10)
Determine Equation by finding "k":
10 = 6.04e^10k
e^(10k) = 1.6556...
10k = ln(1.6556)
k = 0.05416
Equation is I(t) = 6.04e^(0.05416t)
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When does I(t) = 9 million ?
9 = 6.04e^(0.05416t)
e^(0.05416t) = 1.49
0.05416t = ln(1.49)
t = 7.36 years after the year 2000
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Palistinians: (0,3.2), (50,12)
Determine Equation by finding "k":
12 = 3.2*e^(10k)
e^(10k) = 3.75
10k = ln3.75
k = 0.1322..
Equation is P(t) = 3.2e^(0.1322t)
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When does P(t) = 9 million?
9 = 3.2e^(0.1322t)
2.8125 = e^(0.1322t)
0.1322t = ln(2.8125)
t = 7.822
P(t) will reach 9 million 7.822 years after the year 2000
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Cheers,
Stan H.
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