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A town has a population of 14000 and grows at 5% every year. What will be the population after 14 years, to the nearest whole number?
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Verified Answer :

GinnyAnswer

Certainly! To solve this problem, we need to calculate the future population of the town based on exponential growth, using the formula for compound interest.

The formula for compound growth is:

\(\[ P = P_0 \times (1 + r)^t \]\)

where:
- \(\( P \)\) is the future population.
- \(\( P_0 \)\) is the initial population.
- \(\( r \)\) is the annual growth rate.
- \(\( t \)\) is the number of years.

Given:
- Initial population (\(\( P_0 \)\)) = 14,000
- Annual growth rate (\(\( r \)\)) = 0.05 (which is 5%)
- Number of years (\(\( t \)\)) = 14

Let's calculate step-by-step:

1. Initial Population: \(\( P_0 = 14,000 \)\)
2. Growth Rate: \(\( r = 0.05 \)\)
3. Number of Years: \(\( t = 14 \)\)

Plug these values into the formula:

\(\[ P = 14,000 \times (1 + 0.05)^{14} \]\)

First, calculate \(\( 1 + 0.05 \)\):

\(\[ 1 + 0.05 = 1.05 \]\)

Next, raise 1.05 to the power of 14:

\(\[ 1.05^{14} \approx 1.979 \]\)

Now, multiply this result by the initial population:

\(\[ P \approx 14,000 \times 1.979 \]\)

\(\[ P \approx 27,706 \]\)

Hence, the population after 14 years, rounded to the nearest whole number, will be approximately 27,706.

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