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12 July, 16:31

The population of Guatemala in 2000 was 12.7 million.

1. Assuming exponential growth, what would be the size of the population after time t (measured in years after 2000) if the population was 30 million in 2020? Answer (in millions) : P (t) =

2. Assuming exponential growth, what would be the size of the population after time t (measured in years after 2000) if the population was 30 million in 2125?

Answer (in millions) : P (t) =

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Answers (1)
  1. 12 July, 18:18
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    Since the population of Guatemala follows an exponential growth, therefore the equation describing the population over time should be in the form:

    p = p0 (1 + r) ^t

    where,

    p = is the population at specified time t

    p0 = is the initial population (measured starting year 2000) = 12.7 m

    r = the growth rate

    t = time in years

    A. Calculating for the growth rate r when p = 30 and t = 20:

    30 = 12.7 (1 + r) ^20

    1 + r = (30 / 12.7) ^ (1/20)

    r = (30 / 12.7) ^ (1/20) - 1

    r = 0.0440

    So the equation is:

    p = p0 (1.0440) ^t

    B. Calculating for the growth rate r when p = 30 and t = 125:

    30 = 12.7 (1 + r) ^125

    1 + r = (30 / 12.7) ^ (1/125)

    r = (30 / 12.7) ^ (1/125) - 1

    r = 0.0069

    So the equation is:

    p = p0 (1.0069) ^t
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