A city has a population of 360.000 people. Suppose that each year the population grows by 7,25%. What will the population be after 14 years?

1. Break Down the Problem

We need to find the population after 14 years given an initial population of 360,000 and a growth rate of 7.25% per year. The formula for population growth is:

$P = P_0 (1 + r)^t$

where:

• $P$ = future population
• $P_0$ = initial population
• $r$ = growth rate (as a decimal)
• $t$ = number of years

2. Relevant Concepts

1. Identify the initial population $P_0 = 360,000$
2. Convert the growth rate from percentage to decimal: $r = \frac{7.25}{100} = 0.0725$
3. Set the time period $t = 14$ years

3. Analysis and Detail

Using the population growth formula:

$P = 360,000 \times (1 + 0.0725)^{14}$

Now we will calculate:

$P = 360,000 \times (1.0725)^{14}$

Calculating $(1.0725)^{14}$:

$(1.0725)^{14} \approx 2.6943$

Now substituting back into the formula:

$P \approx 360,000 \times 2.6943 \approx 969,948$

4. Verify and Summarize

To verify, we can separately calculate:

1. Calculate $(1.0725)^{14}$ using a calculator which should confirm $\approx 2.6943$.
2. Then multiply by the initial population:

$360,000 \times 2.6943 = 969,948$

This confirms that the calculation is consistent.

Final Answer

The population after 14 years will be approximately 969,948 people.