We need to find the population of the city in the year 2013.
First, we identify our initial population and our growth rate:
- The initial population in 2012 is 6.17 million.
- The growth rate is 1.87% per year.
We can represent the growth rate as a decimal for our calculations by dividing it by 100. So, 1.87% becomes 0.0187.
Next, we're going to use the formula for exponential growth, which is:
population_final = population_initial * e^(growth_rate*time)
Here,
- 'e' is Euler's number, a mathematical constant approximately equal to 2.71828. 'e' is the base of the natural logarithm.
- 'time' represents the number of periods for which the population grows. In this case, since we're calculating the population for 2013 based on the population in 2012, the time is 1 year.
Plugging our numbers into the formula:
population_2013 = 6.17 * e^(0.0187*1)
Using Euler's number for 'e', we solve the equation:
population_2013 = 6.17 * 1.018861821223
Finally, we find that the population of the city in the year 2013 was approximately 6.29 million.