Unformatted text preview: a function of x. Let’s assume that the Cobb-Douglas production model
for the country of Sasquatchia is P = 1.23x0.4 y 0.6 .
(a) Let P = 300 and solve for y in terms of x. If x = 100, what is y ?
(b) Graph the isoquant 300 = 1.23x0.4 y 0.6 . What information does an ordered pair (x, y )
which makes P = 300 give you? With the help of your classmates, ﬁnd several diﬀerent
combinations of labor and capital all of which yield P = 300. Discuss any patterns you
9. According to Einstein’s Theory of Special Relativity, the observed mass m of an object is a
function of how fast the object is traveling. Speciﬁcally,
m(x) = mr
c2 where m(0) = mr is the mass of the object at rest, x is the speed of the object and c is the
speed of light.
(a) Find the applied domain of the function.
(b) Compute m(.1c), m(.5c), m(.9c) and m(.999c).
(c) As x → c− , what happens to m(x)?
(d) How slowly must the object be traveling so that the observed mass is no greater than
100 times its mass at rest?
10. Show that 3 2 is an irrational number by ﬁrst showing that it is a zero of...
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