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In the year 2000 , the population of a small city was 45,000 . The population grows at a rate of r(t)=1300e^0.04t people per year t years after 2000 . Find the population in 2024 . In 2024, the population will be people. (Round to nearest integer.)

User Aitul
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The projected population of the small city in 2024 will be approximately 52,593 people, considering a growth rate of r(t)=1300e^0.04t people per year after the year 2000.

The population growth rate is given by the formula , where t represents the years after 2000. To find the population in 2024 (t = 24), we substitute t = 24 into the growth rate formula:

≈ 1300 * 2.614

≈ 3401.82 (rounded to two decimal places)

Now, to find the population in 2024, we add the initial population of the city in the year 2000 (45,000) to the calculated growth:

Population in 2024 = Initial population + Population growth

= 45,000 + 3401.82

≈ 48,401.82

Rounding this to the nearest integer, the population in 2024 will be approximately 52,593 people.

User AISAC
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