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Unformatted text preview: $920 (E) more than $920 29. The supply function for oil is given (in dollars) by S (q ), and the demand function is given (in dollars)
by D(q )
S (q ) = q 2 + 13q ;
D(q ) = 1054 − 15q − q 2 .
(i) Graph the supply and demand curves on the same axes. (ii) Find the point at which supply and demand are in equilibrium. (iii) Find the consumers’ surplus. (iv) Find the producers’ surplus. 30. The function f (x) = 1000x − 100x2 represents the rate of ﬂow of money in dollars per year. Assume
a 10year period at 4% compounded continuously.
(i) Find the present value of the money ﬂow at the end of 10 years. (ii) Find the accumulated amount of money ﬂow at the end of 10 years. 31. Find the present value of a continuous stream of income over 6 years when the rate of income is constant
at $33,000 per year and the interest rate is 4%.
The present value is
(A) less than $175,000 (B) between $175,000 and $180,000 (C) between $180,000 and $185,000 (D) between $185,000 and $190,000 (E) more than $190,000 32. The rate of a continuous money ﬂow starts at $1100 and increases exponentially at 3% per year for 5
years. Find the present value if interest earned is 4% compounded continuously.
(A) less than $5000 (B) between $5000 and $5400 (C) between $5400 and $5800 (D) between $5800 and $6200 (E) more than $6200 Formulas You Might Find Useful I = A= A = P ert rE = f ( x) = d
[u(x) · v (x)]
dx = u( x) · v ( x) + v ( x) · u ( x) dx
[a ]
dx = (ln a)ax E = p dq
−·
q dp xn dx = xn+1
+C
n+1 x−1 dx = ln x + C P.S. = = er − 1 = f (g (x)) · g (x) = v ( x) · u ( x) − u( x) · v ( x)
[v (x)]2 = 1
(ln a)x q = akx dx = akx
+C
k (ln(a)) C.S. = rE
d
[f (g (x))]
dx
d u( x)
dx v (x)
d
[loga (x)]
dx P =
r mt
P 1+
m
r m
−1
1+
m P rt 2f M
k q0 (D(q ) − p0 ) dq 0
T f ( t) e
0 −rt dt A = lim h→0 e f ( x + h) − f ( x )
h q0
0 rT (p0 − S (q )) dq
T
0 f (t)e−rt dt...
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 Fall '09
 JESS
 Math, Calculus

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