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13 March, 02:21

The function f (x) = 125 (0.9) x models the population of a species of fly in millions after x years.

How does the average rate of change between years 11 and 15 compare to the average rate of change between years 1 and 5?

The average rate of change between years 11 and 15 is about 13 the rate between years 1 and 5.

The average rate of change between years 11 and 15 is about 3 times the rate between years 1 and 5.

The average rate of change between years 11 and 15 is about 12 the rate between years 1 and 5.

The average rate of change between years 11 and 15 is about 2 times the rate between years 1 and 5.

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  1. 13 March, 04:04
    0
    Given that the population is modeled by:

    f (x) = 125 (0.9) ^x

    the average rate of change will be as follows:

    Year 11 and 15:

    f (11) = 125 (0.9) ^11

    =39.226

    f (15) = 125 (0.9) ^15

    =25.736

    rate of change = (25.736-39.226) / (15-11)

    =-3.37

    year 1 and 5

    f (1) = 125 (0.9) ^1

    =112.5

    f (5) = 125 (0.9) ^5

    =73.811

    rate of change:

    (73.811-112.5) / 4

    =-9.67

    dividing the two results of rate of change we get:

    -9.67/-3.37

    =2.97-=3

    From the above we conclude that the average rate of change between year 1 to 5 is above 3 times that of year 11 to year 15
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