SOLUTION: In​ 2012, the population of a city was 6.97 million. The exponential growth rate was ​3.87% per year. ​a) Find the exponential growth function. ​b) Estimate the populatio

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Question 1198712: In​ 2012, the population of a city was 6.97 million. The exponential growth rate was ​3.87% per year.
​a) Find the exponential growth function.
​b) Estimate the population of the city in 2018.
​c) When will the population of the city be 10 million?
​d) Find the doubling time.

Answer by Shin123(626)   (Show Source): You can put this solution on YOUR website!
a) If the city grows at 3.87% per year, that is equivalent to multiplying by 1.0387. Therefore, the equation is , where is the population, and is the number of years after 2012.
b) 2018 is 6 years after 2012, so we would have . Plugging this into our equation, we get . We can simply plug this into a calculator to get .
c) Since is the population, we can plug in 10 million for and solve for .
We have the equation . Dividing both sides by , we get . Taking the natural log of both sides, we get . Using logarithm rules to take the exponent out, we get . Dividing both sides by , we get . Plugging this into a calculator, we get . Since is the number of years after 2012, the population will be 10 million in 2021.
d) To find the doubling time, we can solve the equation , since is how much the population is growing. We can take the natural log of both sides to get . We can use logarithm rules to take out the exponent, which will give . We can divide both sides by to get . Finally, we can plug this into a calculator to get .

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