To find the projected population of Dover City in 2050, we start with the initial population in 2010 and apply the given growth rate over the 4 decades to reach the year 2050.
Here are the step-by-step calculations:
1. Initial population in 2010: 1,200,000
2. Growth rate: The city's population grows at 3.1% per decade, which means a growth rate of 0.031 when expressed as a decimal.
3. Number of decades from 2010 to 2050: 4
To calculate the population at the end of each decade, we will apply the compound interest formula, which is also applicable for population growth:
Population after n decades = Initial population (1 + growth rate) n
Here, n is the number of periods the growth rate is applied.
Using this formula, we calculate the projected population in the year 2050:
Projected population in 2050 = 1,200,000 (1 + 0.031) 4
4. We need to calculate the result of (1 + 0.031) 4 first, which is the growth multiplier over the 4 decades.
5. Now we multiply the initial population by this growth multiplier to get the projected population.
After doing the calculation (which we treat as if it's already given), the projected population of Dover City in 2050 is determined to be approximately 1,355,863 people.
So, in conclusion, the projected population of Dover City in 2050, after accounting for the 3.1% growth every decade over 4 decades, is approximately 1,355,863.
