Quiz 4NAMES_World's Best _Student____________________________
1) Let t(h) be the temperature in degrees Celsius at a height h (in meters)
above the surface of the earth. What do each of the following quantities
mean to a sky diver? Explain using complete sentences. Give units for the
quantities.
(a) t(1000) =22.1 At 1000 meters the temp is 22.1 degrees
(b) t ' (20)=2.18
(Perhaps the decimal place Is misplaced-fix it to
make this a more reasonable value)
t'(20)=-0.0218 deg/meter. Since temps decrease as altitude increases this
should be negative.Expecting 2.18 degrees each meter seems pretty
extreme.
(c) t(h) + 20
SKIPPED!
(d) h such that t ' (h) = 20 h represents the height at which the temp is
changing at the rate of 20 degrees per meter of increased altitude
(e) Make up a reasonable value for t(1000) and t ' (1000) and use your value
to estimate t(900) and t(1100)
t(1000)=22.1 degrees and let t'(1000)=-.02 degrees/meter. ie every
additional meter of height reduces the temp by .02 degrees. Thus going up to
1100 meters means a decrease of 100(-.02) degrees=-2 degrees. So
t(1100)=20.1. Similarly t(900)= 24.1 degrees.
2) Let L(r) be the amount of lumber, in board-feet, produced from a tree of
radius r (measured in inches). Interpret the
following in practical terms, giving units. Use complete sentences.
(a) L(6) =1200
A tree of radius 6" produces 1200 board feet of lumber
(b) L ' (24)=82 If a tree has radius 24 inches each additional Inch produces
82 more board feet
(c) r such that L(r) = 100 The radius of tree that produces 100 board feet
(d) r such that L ' (r) = 10 The radius of tree at whichh each additional inch
produces 10 additional board feet.
(e) Use L(24)=1200 and L ' (24)=82 to find the equation of the line tangent
to the curve y=L(r) at the point y=1200, r=24
y-1200=82(r-24)