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The question is

The world population in 2000 was approximately 6.08 billion. The annual rate of increase was about 1.26%. The function that models this is $$ y = 6.08(10)^{.0052t}$$ where y represents the population in billions and t is the time in years after 2000. Write and solve a logarithmic equation to determine what year the world population will exceed 7.5 billion.

So is the question asking me to convert the given equation into logarithmic equation than $$ 7.05 = 6.08(10)^{.0052t} $$ ( 7.5 billion is y right?) $$ 7.05/6.08 = 10^{.0052t} $$ $$ 1.15 = 10^{.0052t} $$ $$ log(1.15) =.0052t $$ How would i even solve after that? is the way I've done so far good? how would i proceed after this than?

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Hint:

How do you solve the equation $$15 = 0.0052 t?$$

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  • $\begingroup$ divide by .0052 $\endgroup$ – MATH ASKER Nov 6 '15 at 1:02
  • $\begingroup$ @MATHASKER ..There you go. $\endgroup$ – 5xum Nov 6 '15 at 1:03
  • $\begingroup$ wait how did the .0052t go down from the exponent in the queston? $\endgroup$ – MATH ASKER Nov 6 '15 at 1:03
  • $\begingroup$ @MATHASKER That's how logarithms work! $\log(10^x) = x$ $\endgroup$ – 5xum Nov 6 '15 at 1:04
  • $\begingroup$ Oh okay but even if i go on to solve after that i still woulnd't get the right answer? did i do the steps correctly? $\endgroup$ – MATH ASKER Nov 6 '15 at 1:05

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