NYU Polytechnic School Of Engineering MA 1154 WORKSHEET # 3

NYU Polytechnic School Of Engineering
MA 1154
WORKSHEET # 3
Date:
Print Name:
Signature:
Section:
Instructor: Dr. Manocha
ID #:
Directions: Complete all questions clearly and neatly. You must show all work to have credit.
Unclear work will not be graded. THIS IS A CRUCIAL HOMEWORK UNDERSTAND IT
WELL FOR YOUR NEXT EXAM.
Problem Possible
1
10
2
10
3
10
4
10
5
10
6
10
7
10
8
10
9
10
10
10
Total
100
Points
Your signature:
(1) Use the properties of exponents to simplify the given expression.
(a) (x2 y −3 z)3
(b)
x3 y −2
z4
1/6
Your signature:
(2) Solve for x:
x−1
1
2
= 23−2x
(a)
8
1−3x2
1
(b)
= 34x
9
Your signature:
(3) Find the present value of $10, 000 over a term of 5 years at an annual interest rate of
7% if interest is compounded:
(a) Annually
(b) Quarterly
(c) Daily (use 365 days)
(d) Continuously
Your signature:
(4) Esmeralda needs $5, 000 for a trip to Peru when she graduates from college in 4 years.
How much must she invest now at an annual interest rate of 5% compounded continuously to achieve her goal?
Your signature:
(5) In terms of effective interest rate, order the following nominal rate investments from
lowest to highest:
(a) 4.87% compounded quarterly
(b) 4.85% compounded monthly
(c) 4.81% compounded daily (365 days)
(d) 4.79% compounded continuously
Your signature:
(6) It is estimated that t years after 2005, the population of a certain country will be P (t)
million people where
P (t) = 2 · 50.018t
(a) What was the population in 2005?
(b) What will the population be in 2015?
Your signature:
(7) Evaluate each of the following expressions:
(a) e3
ln 2−2 ln 5
√
e3 e
(b) ln 1/3
e
Your signature:
(8) Simplify each of the following:
2
x (3 − x)2/3
(a) ln √
x2 + x + 1
(b) ln
√
4
x
√
x3 1 − x2
Your signature:
(9) Solve for x:
(a) 5 = 3 ln x −
(b)
1
ln x
2
25e0.1x
= 10
e0.1x + 3
Your signature:
(10) A manufacturer determines that the supply function for x units of a particular commodity is S(x) = ln(x + 2) and the correspinding demand function is
D(x) = 10 − ln(x + 1).
(a) Find the demand price p = D(x) when the level of production is x = 10 units.
(b) Find the supply price p = S(x) when x = 100 units.
(c) Find the level of production and unit price that correspond to market equilibrium
(where supply = demand).