# A researcher analyses the MMR (measles, mumps and rubella) vaccination coverage rates from 1991 onwards. She claims that the percentage vaccination rates between 1995 and 2004 can be modeled by the...

A researcher analyses the MMR (measles, mumps and rubella) vaccination coverage rates from 1991 onwards. She claims that the percentage vaccination rates between 1995 and 2004 can be modeled by the equation:

y=-1.52x +99.16 `4<=x<=13`

Find the percentage vaccination rate in 2004, when x=9, according to this model five answer correct to one decimal, then explain the inequality that follows the equation.

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A researcher analyses the MMR (measles, mumps and rubella) vaccination coverage rates from 1991 onwards. She claims that the percentage vaccination rates between 1995 and 2004 can be modeled by the equation:

y=-1.52x +99.16 for `4<=x<=13 `

(a) To find the predicted percentage vaccinated in 2004, or when x=9, substitute x=9 into the equation to get:

y=-1.52(9)+99.16=85.48 or approximately 85.5%.

(b) Note that there is a restriction on the domain for the function. Without this restriction the graph is a line. If negative values for x are interpreted as years before 1991 then there is a time when more than 100% of the population is vaccinated. Also, the rate of vaccination drops below zero after 65 years. These cases obviously do not make sense.

The formula given models the rate of vaccination over a specific time period, namely from 1995 to 2004. The variable is defined as time, in years, after 1991. So the restriction `4<=x<=13 ` indicates that the model is only effective for the years 1991+4 to 1991+13 or 1995 to 2004.

The graph of the equation y=-1.52x +99.16 is:

Substituting the value x = 9. the percentage vaccination rate is

y=-1.52x +99.16

y=-1.52(9) +99.16

y = 85.48 = 85.5

The inequality expressions shows that the value of x lies between 4 and 13,

`4 <=9 <= 13`