Money Stock Exercises 97–100 are based on the following demand function for money (taken from a question on the GRE Economics Test): M d = 2 × y 0.6 × r − 0.3 × p , Where M d = demand for nominal money balances (money stock y = real income r = an index of interest rates p = an index of prices. These exercises also use the idea of percentage rate of growth: Percentage rate of growth of M = Rate of growth in M M = d M / d t M . (From the GRE Economics Test) If the interest rate and price level are to remain constant while real income grows at 5% per year, the money stock must grow at what percent per year?
Money Stock Exercises 97–100 are based on the following demand function for money (taken from a question on the GRE Economics Test): M d = 2 × y 0.6 × r − 0.3 × p , Where M d = demand for nominal money balances (money stock y = real income r = an index of interest rates p = an index of prices. These exercises also use the idea of percentage rate of growth: Percentage rate of growth of M = Rate of growth in M M = d M / d t M . (From the GRE Economics Test) If the interest rate and price level are to remain constant while real income grows at 5% per year, the money stock must grow at what percent per year?
Money Stock Exercises 97–100 are based on the following demand function for money (taken from a question on the GRE Economics Test):
M
d
=
2
×
y
0.6
×
r
−
0.3
×
p
,
Where
M
d
=
demand for nominal money balances (money stock
y
=
real income
r
=
an index of interest rates
p
=
an index of prices. These exercises also use the idea ofpercentage rate of growth:
Percentage rate of growth of M
=
Rate of growth in
M
M
=
d
M
/
d
t
M
.
(From the GRE Economics Test) If the interest rate and price level are to remain constant while real income grows at 5% per year, the money stock must grow at what percent per year?
5. [-/1 Points]
DETAILS
MY NOTES
SESSCALCET2 6.5.AE.003.
y
y= ex²
0
Video Example
x
EXAMPLE 3
(a) Use the Midpoint Rule with n = 10 to approximate the integral
कर
L'ex²
dx.
(b) Give an upper bound for the error involved in this approximation.
SOLUTION
8+2
1
L'ex² d
(a) Since a = 0, b = 1, and n = 10, the Midpoint Rule gives the following. (Round your answer to six decimal places.)
dx Ax[f(0.05) + f(0.15) + ... + f(0.85) + f(0.95)]
0.1 [0.0025 +0.0225
+
+ e0.0625 + 0.1225
e0.3025 + e0.4225
+ e0.2025
+
+ e0.5625 €0.7225 +0.9025]
The figure illustrates this approximation.
(b) Since f(x) = ex², we have f'(x)
=
0 ≤ f'(x) =
< 6e.
ASK YOUR TEACHER
and f'(x) =
Also, since 0 ≤ x ≤ 1 we have x² ≤
and so
Taking K = 6e, a = 0, b = 1, and n = 10 in the error estimate, we see that an upper bound for the error is as follows. (Round your final
answer to five decimal places.)
6e(1)3
e
24(
=
≈
2. [-/1 Points]
DETAILS
MY NOTES
SESSCALCET2 6.5.015.
Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.)
ASK YOUR TEACHER
3
1
3 +
dy, n = 6
(a) the Trapezoidal Rule
(b) the Midpoint Rule
(c) Simpson's Rule
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Watch It
This question builds on an earlier problem. The randomized numbers may have changed, but have your work for the previous problem available to help with this one.
A 4-centimeter rod is attached at one end to a point A rotating counterclockwise on a wheel of radius 2 cm. The other end B is free to move back and forth along a horizontal bar that goes through the center of the wheel. At time t=0 the rod is situated as in the diagram at the left below. The
wheel rotates counterclockwise at 1.5 rev/sec. At some point, the rod will be tangent to the circle as shown in the third picture.
B
A
B
at some instant, the piston will be tangent to the circle
(a) Express the x and y coordinates of point A as functions of t:
x= 2 cos(3πt)
and y= 2 sin(3πt)
(b) Write a formula for the slope of the tangent line to the circle at the point A at time t seconds:
-cot (3πt)
(c) Express the x-coordinate of the right end of the rod at point B as a function of t: 2 cos(3πt) +41/1
(d) Express the slope of the rod…
Chapter 11 Solutions
Student Solutions Manual for Waner/Costenoble's Finite Math and Applied Calculus, 7th
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Time Series Analysis Theory & Uni-variate Forecasting Techniques; Author: Analytics University;https://www.youtube.com/watch?v=_X5q9FYLGxM;License: Standard YouTube License, CC-BY