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Suppose a city with a population of 800,000 has been growing at a rate of 2% per year. If this rate continues, find the population of this city in 15 years.

a) 916,400
b) 928,100
c) 940,000
d) 952,800

Answer :

Final answer:

Using the exponential growth formula, P(t) = P0 (1 + r)^t, the population of a city with an initial population of 800,000 growing at a rate of 2% per year will be approximately 1,079,887 after 15 years.

Explanation:

The student's question relates to calculating the future population size of a city that is experiencing exponential growth at a rate of 2% per year. To find the population of the city in 15 years, we need to apply the formula for exponential growth, which is:

P(t) = P0 (1 + r)^t

Where:

  • P(t) = the population at time t
  • P0 = the initial population size
  • r = the growth rate per period (expressed as a decimal)
  • t = the number of periods (years in this case)

Using the information provided:

  • P0 = 800,000 people
  • r = 2% per year = 0.02 (as a decimal)
  • t = 15 years

We can now calculate the population after 15 years:

P(15) = 800,000 (1 + 0.02)^15

P(15) = 800,000 (1.02)^15

P(15) = 800,000 (1.3498588075760032)

P(15) = 1,079,887.0460608026 ≈ 1,079,887

Therefore, the population of the city in 15 years will be approximately 1,079,887 people. This means none of the options provided (a, b, c, d) are correct.

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