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3 January, 18:17

The population of a small rural town in the year 2006 was 2,459. The population can be modeled by the function below, where f (x) is the number of residents and t is the number of years elapsed since 2006. Using the information given above, complete the following statements. The percent change is %. The percent change represents.

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  1. 3 January, 20:57
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    f (x) = 2,459 (0.92) ^t

    Using the information given above, complete the following statements. The percent change is %. The percent change represents.

    f (x) = 2,459 (0.92) ^t

    Given equation is an exponential function and in the form of f (x) = a (1-r) ^x

    Where 'a' is the initial population

    'r' is the decay rate

    'x' is the time

    f (x) = a (1-r) ^x

    Given function is f (x) = 2,459 (0.92) ^t

    1 - r = 0.92

    r = 1 - 0.92

    r = 0.08

    r = 0.08 %

    Percentage change = 0.08%

    Percentage change represents the decay rate.
  2. 3 January, 22:04
    0
    8%, the rate at which the population is decreasing.

    Step-by-step explanation:

    Look at the equation f (x) = 2,459 (0.92) ^t

    0.92 represents the rate of change.

    Because 0.92 is less than 1, it represents a decrease.

    To calculate the rate of decay, subtract 0.92 from 1 (1 - 0.92 = 0.08)

    To convert the rate of decay to percent, move the decimal to the right two spaces.

    The answer is 8%, which represents the rate at which the population is decreasing.
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