Final answer:
By applying the exponential growth formula, the population of a city that starts with 400,000 people and grows at a rate of 6% per year will be around 990,800 in 16 years.
Step-by-step explanation:
To find the population of the city in 16 years given a starting population of 400,000 and a growth rate of 6% per year, we use the formula for exponential growth P = P_0(1 + r)^t, where P is the final population, P_0 is the initial population, r is the growth rate (in decimal form), and t is the time in years.
Substituting the given values into the formula:
- P_0 = 400,000
- r = 0.06 (6% growth)
- t = 16 years
The calculation will be:
P = 400,000(1 + 0.06)¹⁶
Conducting the calculations:
P = 400,000(1.06)¹⁶
P ≈ 400,000(2.477)
P ≈ 990,800
Therefore, if the growth rate continues, the population of the city in 16 years will be approximately 990,800.