anonymous
  • anonymous
can anyone help me with Exponential Growth?
Mathematics
chestercat
  • chestercat
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amistre64
  • amistre64
can try
anonymous
  • anonymous
A country's population in 1994 was 107 million. In 1997 it was 112 million. Estimate the population in 2008 using the exponential growth formula. Round your answer to the nearest million. \[P = Ae ^{kt}\]
amistre64
  • amistre64
this is Population = inital size * e^(rate of change per year * years) right?

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anonymous
  • anonymous
i do believe so
amistre64
  • amistre64
122 = 107.e^3r 122 ---- = e^3r 107 ln(122/107) = 3r r = 1/3 ln(122/107) = .04373... about 4.373 %
amistre64
  • amistre64
P = 107.e(.04373(3)) = 121.999
amistre64
  • amistre64
lol..... well thats right; now we just gotta adjust the time to 2008
amistre64
  • amistre64
P = 107.e(.04373(14)) = 197.36....
anonymous
  • anonymous
it says the answer is 132
amistre64
  • amistre64
did i get my years wrong? 2008 1994 ----- 14 nope thats right...
amistre64
  • amistre64
it could be a truncation error; i should try it with all the decimals then and see
amistre64
  • amistre64
107 * (e^((1 / 3) * ln(122 / 107) * 14)) = 197.365857
amistre64
  • amistre64
ahhhh i see what i did; i use 122..... the questions asks for 112
amistre64
  • amistre64
yeah, i gotta learn to read :) 107 * (e^((1 / 3) * ln(112 / 107) * 14)) = 132.416952

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