Question

Suppose a city with population of 700,000 has been growing at a rate of 6​% per year. If this rate​ continues, find the population of this city in 22 years.

The population in 22 years will be approximately
. ​(Round to the nearest whole number as​ needed and use commas.)

Answer 1

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**.