document.write( "Question 1198712: In 2012, the population of a city was 6.97 million. The exponential growth rate was 3.87% per year.
\n" ); document.write( "a) Find the exponential growth function.
\n" ); document.write( "b) Estimate the population of the city in 2018.
\n" ); document.write( "c) When will the population of the city be 10 million?
\n" ); document.write( "d) Find the doubling time.
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Algebra.Com's Answer #832338 by Shin123(626) $\"\"$ $\"About$

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a) If the city grows at 3.87% per year, that is equivalent to multiplying by 1.0387. Therefore, the equation is $\"P=6970000%2A1.0387%5Et\"$ , where $\"P\"$ is the population, and $\"t\"$ is the number of years after 2012.
\n" ); document.write( "b) 2018 is 6 years after 2012, so we would have $\"t=6\"$ . Plugging this into our equation, we get $\"P=6970000%2A1.0387%5E6\"$ . We can simply plug this into a calculator to get $\"P=highlight%288753335%29\"$ .
\n" ); document.write( "c) Since $\"P\"$ is the population, we can plug in 10 million for $\"P\"$ and solve for $\"t\"$ .
\n" ); document.write( "We have the equation $\"10000000=6970000%2A1.0387%5Et\"$ . Dividing both sides by $\"6970000\"$ , we get $\"1.0387%5Et=1.43472023\"$ . Taking the natural log of both sides, we get $\"ln%281.0387%5Et%29=ln%281.43472023%29\"$ . Using logarithm rules to take the exponent out, we get $\"t%2Aln%281.0387%29=ln%281.43472023%29\"$ . Dividing both sides by $\"ln%281.0387%29\"$ , we get $\"t=ln%281.43472023%29%2Fln%281.0387%29\"$ . Plugging this into a calculator, we get $\"t=9.50672957\"$ . Since $\"t\"$ is the number of years after 2012, the population will be 10 million in 2021.
\n" ); document.write( "d) To find the doubling time, we can solve the equation $\"1.0387%5Et=2\"$ , since $\"1.0387%5Et\"$ is how much the population is growing. We can take the natural log of both sides to get $\"ln%281.0387%5Et%29=ln%282%29\"$ . We can use logarithm rules to take out the exponent, which will give $\"t%2Aln%281.0387%29=ln%282%29\"$ . We can divide both sides by $\"ln%281.0387%29\"$ to get $\"t=ln%282%29%2Fln%281.0387%29\"$ . Finally, we can plug this into a calculator to get $\"t=highlight%2818.25516027%29\"$ . \n" ); document.write( "

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