– HEALTHY AVERAGE SYSTOLIC BLOOD

PRESSURE IS ESTIMATED BY P=0.01A

SQUARED=0.05A + 107 WHERE “A” IS THE AGE IN YEARS AND P IS THE PRESSURE

IN MILLILITERS OF MERCURY. NUMBER 1, WHAT IS THE HEALTHY

AVERAGE SYSTOLIC BLOOD PRESSURE OF A 34-YEAR-OLD

TO THE NEAREST 10th? SO TO DETERMINE THE PRESSURE, WE’LL SUBSTITUTE 34 FOR “A”

INTO OUR EQUATION. SO P OF 34 IS GOING TO BE EQUAL TO 0.01 x 34 SQUARED

+ 0.05 x 34 + 107. AND WE’LL GO AHEAD

AND USE THE CALCULATOR TO DETERMINE THIS VALUE. SO 0.01 x 34 SQUARED

+ 0.05 x 34 + 107. NOW, THEY WANT US TO ROUND

TO THE NEAREST 10th, SO THIS WILL BE APPROXIMATELY

120.3 MILLILITERS OF MERCURY. NUMBER 2 IS GOING TO BE A LITTLE

BIT MORE INVOLVED. IF A HEALTHY PERSON

HAS A SYSTOLIC BLOOD PRESSURE OF 132.4 MILLILITERS OF MERCURY, WHAT IS THEIR AGE

TO THE NEAREST YEAR? SO WE’RE GOING TO NEED SOME MORE

ROOM FOR THIS. LET’S GO AHEAD

AND GO TO THE NEXT SLIDE. FOR THIS PROBLEM, THEY’RE GIVING

US THE PRESSURE, P, AND WE NEED TO SOLVE FOR “A.” SO WE NEED TO SOLVE

THE EQUATION 132.4=0.01A SQUARED

+ 0.05A + 107, SO WE HAVE QUADRATIC EQUATION. SO WHAT WE’RE GOING TO DO HERE

IS SET IT EQUAL TO 0 AND USE THE QUADRATIC FORMULA. SO WE’LL START

BY SUBTRACTING 132.4 ON BOTH SIDES OF THE EQUATION, SO WE’LL HAVE 0=0.01A

SQUARED + 0.05A, 107 – 132.4 IS GOING TO BE

NEGATIVE OR MINUS 25.4. AND NOW TO APPLY THE QUADRATIC

FORMULA, “A” IS THE COEFFICIENT

OF THE DEGREE 2 TERM, SO WE’LL HAVE=0.01, B IS THE COEFFICIENT

OF THE DEGREE 1 TERM, 0.05, AND C IS EQUAL TO THE CONSTANT

TERM OF -25.4. NOW USING THE QUADRATIC FORMULA

GIVEN HERE BELOW, WE WILL HAVE X=-B OR -0.05 PLUS OR MINUS THE SQUARE ROOT OF

B SQUARED – 4 x “A” x C ALL OVER 2 x “A”

WHICH WOULD BE 2 x 0.01. NOW ONE THING TO BE AWARE OF

HERE, HERE WE’RE SAYING X EQUALS BUT WE SHOULD RECOGNIZE THAT OUR

EQUATION IS IN TERMS OF “A”, SO THIS IS REALLY “A” EQUALS, NOT TO BE CONFUSED

FOR THIS “A” HERE THAT WOULD BE THE COEFFICIENT

OF THE DEGREE 2 TERM. SO JUST TO AVOID CONFUSION, WE’LL GO AHEAD

AND CONTINUE WITH X. WE’LL HAVE X=-0.05 PLUS OR MINUS

THE SQUARE ROOT OF. NOW, WE’LL DETERMINE

THE DISCRIMINANT HERE AND THIS WOULD BE DIVIDED

BY 2 x 0.01 OR 0.02, SO OUR DISCRIMINANT

WILL BE 0.05 SQUARED – 4 x “A” WHICH IS 0.01 x C

WHICH IS – 25.4, SO WE HAVE 1.0185. NOW REMEMBER, WE ARE GOING

TO HAVE 2 SOLUTIONS HERE. BUT SINCE THIS X VALUE OR “A”

VALUE REPRESENTS THE AGE, WE KNOW THE AGE

CAN’T BE NEGATIVE, SO THE ONLY POSSIBLE SOLUTION

WOULD BE X=-0.05 + THE SQUARE ROOT OF

1.0185 DIVIDED BY 0.02. AND THEY WANT THIS

TO THE NEAREST YEAR, SO NOW WE’LL GO BACK

TO THE CALCULATOR TO DETERMINE

THIS APPROXIMATE VALUE. SO TO DO THIS,

WE’LL HAVE A SET OF PARENTHESES FOR THE NUMERATOR. WE’LL HAVE AN OPEN PARENTHESIS -0.05 + THE SQUARE ROOT

OF 1.0185. NOTICE WE HAVE ONE CLOSED

PARENTHESIS FOR THE SQUARE ROOT AND THE SECOND ONE

FOR NUMERATOR, AND I’M GOING TO DIVIDE THIS

BY 0.02. SO WE HAVE APPROXIMATELY

47.96 YEARS WHICH WOULD ROUND

TO 48 YEARS OF AGE. OKAY I HOPE

YOU FOUND THIS HELPFUL.