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In the year 2000, the population of Town A was 5,000 people. In the year 2010, the population grew to 6,500 people. Assuming the rate of growth was exponential, write down a function P(t) which models the population of Town A as a function of time t-years since the year 2000. What will be the population in the year 2030?

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sqdancefan

Answer:

  • P(t) = 5000·1.3^(t/10)
  • 10,985

Step-by-step explanation:

The population grew by a factor of 6500/5000 = 1.3 in the 10 years between 2000 and 2010, so the exponential function can be written as ...

  P(t) = 5000·1.3^(t/10)

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Then in 30 years, the population will be modeled as ...

  P(30) = 5000·1.3^(30/10) = 5000·2.197

  P(30) = 10,985

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