The table below lists the number of accidental death per 100,000 people in the United States through the past century (from the U.S. Department of Health and Human Services, National Center of...

  1.   The table below lists the number of accidental death per 100,000 people in the United States through the past century (from the U.S. Department of Health and Human Services, National Center of Health Statistics). Use the explanation below the table to find how many deaths will there be in 2010?

Year             1910   1920   1930   1940   1950   1960   1970   1980   1990  2000
Death Rate   84.4   71.2    80.5    73.4   60.3     52.1    56.2   46.5    36.9   34.0

To find the answer, we use a technique called least squares regression.  We begin by entering the data into a TI-83/84 calculator.  We will be using two lists called L1 and L2. Hit the STAT menu and going to EDIT. Enter the last two digits of the first row of the table in L1 (note the year 2000 will be 100 in L1). Then enter the second row into L2.  Then press STAT again and choose CALC.  Then choose item 4 LinReg(ax+b).  Note you get an a and a b back for the line y=ax+b.   What equation did you get? Now find the number of deaths in 2010. Also use your equation to find what year is the death rate predicted to drop below 26 per 100,000 population.      

Asked on by lucyball

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lemjay | High School Teacher | (Level 3) Senior Educator

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Using the TI-83/84 calculator, the equation that describes the relationship between the two sets of data is:

`y=-0.55969697x+90.33333333`

where x represents the number of years since 1900 and y is the number of accidental death per 100,000 in the US.

(A) How many deaths there will be in 2010?

To solve, determine the value of x first. Since the year is 2010, the x will be:

`x=2010-19 00`

`x=110`

Then, plug-in this value of x to the equation above.

`y=-0.55969697(110)+90.33333333`

`y=28.76666663`

Rounding off to nearest hundredth, it becomes:

`y=28.8`

Therefore, there will be 28.8 accidental deaths per 100,000 people in year 2010.

(B)What year is the death rate predicted to drop below 26 per 1000,000 population?

To solve, determine the number of years it take for the y to become 26. To do so, plug-in y=26 to the equation above.

`26=-0.55969697x+90.33333333`  

Then, solve for x.

`26-90.33333333=-0.55969697x`

`(26-90.33333333)/(-0.55969697)=x`

`114.94=x`

Rounding up to nearest whole number, it becomes:

`x=115`

So, it will take 115 years after 1900 for the death rate to become 26 per 100,000 people. And this will occur in year 2015.

Since the equation

`y=-0.55969697x+90.33333333`

tells us that the y decreases as the value of x increases, then after the year 2015, the y values will be below 26.

Thus, it will be after the year 2015 that the predicted death rate will go below 26 per 100,000 population.

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