can anyone help me with Exponential Growth?

Question

amistre64 · Answer

can try

anonymous · Answer

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 · Answer

this is Population = inital size * e^(rate of change per year * years) right?

anonymous · Answer

i do believe so

amistre64 · Answer

122 = 107.e^3r

122
---- = e^3r
107

ln(122/107) = 3r

r = 1/3 ln(122/107) = .04373...  about 4.373 %

amistre64 · Answer

P = 107.e(.04373(3)) = 121.999

amistre64 · Answer

lol..... well thats right; now we just gotta adjust the time to 2008

amistre64 · Answer

P = 107.e(.04373(14)) = 197.36....

anonymous · Answer

it says the answer is 132

amistre64 · Answer

did i get my years wrong?

2008
1994
-----
     14  nope thats right...

amistre64 · Answer

it could be a truncation error; i should try it with all the decimals then and see

amistre64 · Answer

107 * (e^((1 / 3) * ln(122 / 107) * 14)) = 197.365857

amistre64 · Answer

ahhhh  i see what i did; i use 122..... the questions asks for 112

amistre64 · Answer

yeah, i gotta learn to read :)


107 * (e^((1 / 3) * ln(112 / 107) * 14)) = 132.416952