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Blueville has a population of 7000. Its population is increasing at a rate of 1.4%.

Write a function that represents the population as a function of time.

User Nupur
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Final answer:

The population of Blueville, starting at 7000, with a growth rate of 1.4% per year, can be represented by the exponential growth function P(t) = 7000 × (1 + 0.014)^t, where P(t) is the population at time t.

Step-by-step explanation:

To represent the population of Blueville as a function of time with an initial population of 7000 and an annual growth rate of 1.4%, we can use the exponential growth model. This mathematical model is commonly used in demography to estimate population changes over time. The standard form of this model is:

P(t) = P0 × (1 + r)t

Where:

  • P(t) is the population at time t
  • P0 is the initial population
  • r is the annual growth rate (expressed as a decimal)
  • t is the time in years

For Blueville:

  • P0 = 7000 people
  • r = 0.014 (since 1.4% = 0.014)
  • t will be the number of years since the growth began

Thus, the function representing the population growth over time in Blueville is:

P(t) = 7000 × (1 + 0.014)t

Using this function, one can calculate the population of Blueville for any given year, by plugging in the value of t into the equation.

User Bjou
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