To find the population of the city in 22 years given an initial population of 700,000 and an annual growth rate of 6%, we can use the formula for exponential growth:
\[ P(t) = P_0 \times (1 + r)^t \]
where:
- \(P(t)\) is the population after time \(t\),
- \(P_0\) is the initial population,
- \(r\) is the growth rate (as a decimal),
- \(t\) is the number of years.
In this case:
- \(P_0 = 700,000\),
- \(r = 0.06\) (since 6% as a decimal is 0.06),
- \(t = 22\).
Now we can plug the values into the formula:
\[ P(22) = 700,000 \times (1 + 0.06)^{22} \]
Calculating \(1 + 0.06\):
\[ 1 + 0.06 = 1.06 \]
Now calculate \( (1.06)^{22} \):
\[ (1.06)^{22} \approx 3.5836 \quad \text{(using a calculator)} \]
Now multiply this by the initial population:
\[ P(22) \approx 700,000 \times 3.5836 \approx 2,508,520 \]
Therefore, rounding to the nearest whole number, the population in 22 years will be approximately 2,508,520.
So the final answer is:
2,508,520.