SOLUTION: a.a. In 2000, the population of a country was approximately 6.27 million and by 2097it is projected to grow to 16 million. Use the exponential growth model Upper A equals Upper A

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: a.a. In 2000, the population of a country was approximately 6.27 million and by 2097it is projected to grow to 16 million. Use the exponential growth model Upper A equals Upper A       Log On


   



Question 1088780: a.a.
In 2000, the population of a country was approximately 6.27 million and by 2097it is projected to grow to 16 million. Use the exponential growth model Upper A equals Upper A 0 e Superscript ktA=A0ekt​, in which t is the number of years after 2000 and Upper A 0A0 is in​ millions, to find an exponential growth function that models the data.
b.b.
By which year will the population be 1212 ​million?

Answer by josgarithmetic(39620) About Me  (Show Source):
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In 2000, the population of a country was approximately 6.27 million, and by 2097, it is projected to grow to 16 million. Use the exponential growth model Upper A equals Upper A 0 e Superscript kt A=A[o]e^(kt)​, or A=A%5Bo%5De%5E%28kt%29, in which t is the number of years after 2000 and Upper A 0A0 A%5Bo%5D is in​ millions, to find an exponential growth function that models the data.
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16=6.27%2Ae%5E%2897k%29
ln%2816%29=ln%286.27%29%2B97k%2Aln%28e%29
97k=ln%2816%29-ln%286.27%29
k=%28ln%2816%2F6.27%29%29%2F97
highlight_green%28k=0.00966%29

highlight%28A%28t%29=A%5Bo%5D%2Ae%5E%280.00966t%29%29