Many science fiction movies feature animals such as ants, spiders, or apes growing to monstrous sizes and threatening defenseless Earthlings. (Of course, they are in the end defeated by the hero and heroine.) Biologists use power functions as a rough guide to relate body weight and cross-sectional area of limbs to length or height. Generally, weight is thought to be proportional to the cube of length, whereas cross-sectional area of limbs is proportional to the square of length. Suppose an ant, having been exposed to "radiation," is enlarged to 300 times its normal length. (Such an event can occur only in Hollywood fantasy. Radiation is utterly incapable of causing such a reaction.) (a) By how much will its weight be increased? Its weight is increased by a factor of (300 (b) By how much will the cross-sectional area of its legs be increased? The cross-sectional area of its legs is increased by a factor of (4000 (c) Pressure on a limb is weight divided by cross-sectional area. By how much has the pressure on a leg of the giant ant increased? Note: The factor by which pressure increases is given by Factor of increase in weight Factor of increase in area The pressure on a leg increases by a factor of (200

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter4: Polynomials
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Many science fiction movies feature animals such as ants, spiders, or apes
growing to monstrous sizes and threatening defenseless Earthlings. (Of
course, they are in the end defeated by the hero and heroine.) Biologists use
power functions as a rough guide to relate body weight and cross-sectional
area of limbs to length or height. Generally, weight is thought to be
proportional to the cube of length, whereas cross-sectional area of limbs is
proportional to the square of length. Suppose an ant, having been exposed to
"radiation," is enlarged to 300 times its normal length. (Such an event can
occur only in Hollywood fantasy. Radiation is utterly incapable of causing such
a reaction.)
(a) By how much will its weight be increased?
Its weight is increased by a factor of (300
X .
(b) By how much will the cross-sectional area of its legs be increased?
The cross-sectional area of its legs is increased by a factor of
40000
X .
(c) Pressure on a limb is weight divided by cross-sectional area. By how
much has the pressure on a leg of the giant ant increased? Note: The
factor by which pressure increases is given by
Factor of increase in weight
Factor of increase in area
The pressure on a leg increases by a factor of 200
Transcribed Image Text:Many science fiction movies feature animals such as ants, spiders, or apes growing to monstrous sizes and threatening defenseless Earthlings. (Of course, they are in the end defeated by the hero and heroine.) Biologists use power functions as a rough guide to relate body weight and cross-sectional area of limbs to length or height. Generally, weight is thought to be proportional to the cube of length, whereas cross-sectional area of limbs is proportional to the square of length. Suppose an ant, having been exposed to "radiation," is enlarged to 300 times its normal length. (Such an event can occur only in Hollywood fantasy. Radiation is utterly incapable of causing such a reaction.) (a) By how much will its weight be increased? Its weight is increased by a factor of (300 X . (b) By how much will the cross-sectional area of its legs be increased? The cross-sectional area of its legs is increased by a factor of 40000 X . (c) Pressure on a limb is weight divided by cross-sectional area. By how much has the pressure on a leg of the giant ant increased? Note: The factor by which pressure increases is given by Factor of increase in weight Factor of increase in area The pressure on a leg increases by a factor of 200
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