Height-Mass Problem, Second Model The masses of similarly shaped people vary directly with the cube of their height. however, tall people tend to be thinner in proportion to their height than short people. Assume that the masses of people of average build vary with some power of their height, masses and published for boys and girls:
Height Boys Girls
150cm 45kg 41kg
180cm 74kg 67kg
a. Write the particular equation for boys expressing mass in terms of height. Since there are tow unknown constants (the exponent and the proportionality constant), you must substitute both ordered pairs into the equation and solve the resulting system for the constants. You can make the equations linear by taking the logs of both members first.
b. Write another equation for girls, as in part a, above.
c. Predict Sally Forth's mass. She is 173 cm tall. Show that your answer is reasonable by showing that it is between 41 and 67kg.
d. Use the equation for boys to predict Professor Snarff's mass. He is 193cm tall.
e. Professor Snarff is actually 91kg. A person's mass is considered to be "normal" if it is within 5% of that predicted by the model. Is the professor normal, overweight, or underweight? justify your answer....
Height Boys Girls
150cm 45kg 41kg
180cm 74kg 67kg
a. Write the particular equation for boys expressing mass in terms of height. Since there are tow unknown constants (the exponent and the proportionality constant), you must substitute both ordered pairs into the equation and solve the resulting system for the constants. You can make the equations linear by taking the logs of both members first.
b. Write another equation for girls, as in part a, above.
c. Predict Sally Forth's mass. She is 173 cm tall. Show that your answer is reasonable by showing that it is between 41 and 67kg.
d. Use the equation for boys to predict Professor Snarff's mass. He is 193cm tall.
e. Professor Snarff is actually 91kg. A person's mass is considered to be "normal" if it is within 5% of that predicted by the model. Is the professor normal, overweight, or underweight? justify your answer....