Question 1151357
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The "hint" about the form of the equation in the post is "perpendicular" (or "opposite") to the logic of the problem.


The form of the equation, consistent with the post, is <U>THIS exponential function</U>


    N(t) = N*1.012^t,


where "t" is the time in years after 2000 and N = 10 millions (in the year of 2000).


Then you need to find the time "t" in years from the equation


    13 = 10*1.012^t.


Divide both sides by 10


    {{{13/10}}} = 1.012^t,

    1.0.12^t = 1.3


and take the logarithm base 10 from both sides


    t*log(1.012) = log(1.3),

    t = {{{log((1.3))/log((1.012))}}} = 21.995 years = 22 years (approximately).     <U>ANSWER</U>
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Solved, answered and explained.