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QuestionCalculate the average rate of change in active-duty gay servicemember discharges from 1994-1998 and 2001-2006 using points (1994,617), (1998,1163), (2001,1273), (2006,623). Explain the meaning of these rates.

Studdy Solution

STEP 1

Assumptions1. The discharge numbers for the years1994,1998,2001 and2006 are given as (1994,617), (1998,1163), (2001,1273), (2006,623) respectively. . The average rate of change is calculated as the change in the number of discharges divided by the change in years.
3. The average rate of change is rounded to the nearest whole number.

STEP 2

First, we need to calculate the average rate of change for the period from1994 through1998. The formula for the average rate of change isAverage rate of change=Final value−Initial valueFinal year−Initial yearAverage\, rate\, of\, change = \frac{Final\, value - Initial\, value}{Final\, year - Initial\, year}

STEP 3

Now, plug in the given values for the initial and final values and years to calculate the average rate of change for the period from199 through1998.
Average rate of change=1163−6171998−199Average\, rate\, of\, change = \frac{1163 -617}{1998 -199}

STEP 4

Calculate the average rate of change for the period from1994 through1998.
Average rate of change=1163−6171998−1994=136.Average\, rate\, of\, change = \frac{1163 -617}{1998 -1994} =136.

STEP 5

Round the average rate of change to the nearest whole number.
Average rate of change=137Average\, rate\, of\, change =137

STEP 6

Repeat steps2 to5 to calculate the average rate of change for the period from2001 through2006.
Average rate of change=623−12732006−2001Average\, rate\, of\, change = \frac{623 -1273}{2006 -2001}

STEP 7

Calculate the average rate of change for the period from2001 through2006.
Average rate of change=623−12732006−2001=−130Average\, rate\, of\, change = \frac{623 -1273}{2006 -2001} = -130

STEP 8

Round the average rate of change to the nearest whole number.
Average rate of change=−130Average\, rate\, of\, change = -130The average rate of change for the period from1994 through1998 is137, which means that on average, the number of active-duty gay servicemembers discharged from the military for homosexuality under the "don't ask, don't tell" policy increased by137 each year. The average rate of change for the period from2001 through2006 is -130, which means that on average, the number of active-duty gay servicemembers discharged from the military for homosexuality under the "don't ask, don't tell" policy decreased by130 each year.

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