Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.
15th Edition
ISBN: 9781323047620
Author: Barnett, Ziegler, Byleen
Publisher: Pearson Education
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Chapter 8.4, Problem 4MP
To determine
To evaluate: The definite
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Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
There are three options for investing $1150. The first earns 10% compounded annually, the second earns 10% compounded quarterly, and the third earns 10% compounded continuously. Find equations that model each investment growth and
use a graphing utility to graph each model in the same viewing window over a 20-year period. Use the graph to determine which investment yields the highest return after 20 years. What are the differences in earnings among the three
investment?
STEP 1: The formula for compound interest is
A =
nt
= P(1 + − − ) n²,
where n is the number of compoundings per year, t is the number of years, r is the interest rate, P is the principal, and A is the amount (balance) after t years. For continuous compounding, the formula reduces to
A = Pert
Find r and n for each model, and use these values to write A in terms of t for each case.
Annual Model
r=0.10
A = Y(t) = 1150 (1.10)*
n = 1
Quarterly Model
r = 0.10
n = 4
A = Q(t) = 1150(1.025) 4t
Continuous Model
r=0.10
A = C(t) =…
Chapter 8 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.
Ch. 8.1 - Find the degree measure of 1 rad.Ch. 8.1 - Without using a calculator, find: (A)cot 45 (B)cos...Ch. 8.1 - Solve the right triangle in Figure 14. Round side...Ch. 8.1 - Solve the right triangle in Figure 16. Round...Ch. 8.1 - Repeat Example 5 assuming that the man is standing...Ch. 8.1 - Prob. 1EDCh. 8.1 - Prob. 1ECh. 8.1 - In Problems 18, mentally convert each degree...Ch. 8.1 - In Problems 18, mentally convert each degree...Ch. 8.1 - In Problems 18, mentally convert each degree...
Ch. 8.1 - In Problems 18, mentally convert each degree...Ch. 8.1 - In Problems 18, mentally convert each degree...Ch. 8.1 - In Problems 18, mentally convert each degree...Ch. 8.1 - Prob. 8ECh. 8.1 - Prob. 9ECh. 8.1 - Prob. 10ECh. 8.1 - In Problems 916, find the trigonometric ratio by...Ch. 8.1 - Prob. 12ECh. 8.1 - Prob. 13ECh. 8.1 - Prob. 14ECh. 8.1 - In Problems 916, find the trigonometric ratio by...Ch. 8.1 - Prob. 16ECh. 8.1 - Prob. 17ECh. 8.1 - Prob. 18ECh. 8.1 - In Problems 1724, find the exact value without...Ch. 8.1 - Prob. 20ECh. 8.1 - Prob. 21ECh. 8.1 - Prob. 22ECh. 8.1 - In Problems 1724, find the exact value without...Ch. 8.1 - Prob. 24ECh. 8.1 - Prob. 25ECh. 8.1 - Prob. 26ECh. 8.1 - Prob. 27ECh. 8.1 - In Problems 2536, use a calculator set in degree...Ch. 8.1 - Prob. 29ECh. 8.1 - Prob. 30ECh. 8.1 - In Problems 2536, use a calculator set in degree...Ch. 8.1 - Prob. 32ECh. 8.1 - Prob. 33ECh. 8.1 - Prob. 34ECh. 8.1 - In Problems 2536, use a calculator set in degree...Ch. 8.1 - Prob. 36ECh. 8.1 - Prob. 37ECh. 8.1 - Prob. 38ECh. 8.1 - In Problems 3742, use a calculator to find the...Ch. 8.1 - Prob. 40ECh. 8.1 - In Problems 3742, use a calculator to find the...Ch. 8.1 - Prob. 42ECh. 8.1 - Prob. 43ECh. 8.1 - Prob. 44ECh. 8.1 - Prob. 45ECh. 8.1 - Prob. 46ECh. 8.1 - Prob. 47ECh. 8.1 - Prob. 48ECh. 8.1 - Prob. 49ECh. 8.1 - Prob. 50ECh. 8.1 - Prob. 51ECh. 8.1 - Prob. 52ECh. 8.1 - Digital display. An 8-foot-tall digital display...Ch. 8.1 - Prob. 54ECh. 8.1 - Prob. 55ECh. 8.1 - Prob. 56ECh. 8.1 - An angle above the horizontal is called an angle...Ch. 8.1 - An angle above the horizontal is called an angle...Ch. 8.1 - Prob. 59ECh. 8.1 - Prob. 60ECh. 8.2 - Referring to Figure 2, find (A) sin 180(B)...Ch. 8.2 - Find the exact values without using a calculator....Ch. 8.2 - Find the exact values without using a calculator....Ch. 8.2 - Refer to Example 4. (A)Find the exact value of...Ch. 8.2 - Prob. 1EDCh. 8.2 - Prob. 1ECh. 8.2 - Prob. 2ECh. 8.2 - In Problems 18, find the exact value of each...Ch. 8.2 - Prob. 4ECh. 8.2 - In Problems 18, find the exact value of each...Ch. 8.2 - Prob. 6ECh. 8.2 - In Problems 18, find the exact value of each...Ch. 8.2 - Prob. 8ECh. 8.2 - Prob. 9ECh. 8.2 - In Problems 924, find the exact value of each...Ch. 8.2 - In Problems 924, find the exact value of each...Ch. 8.2 - Prob. 12ECh. 8.2 - Prob. 13ECh. 8.2 - Prob. 14ECh. 8.2 - Prob. 15ECh. 8.2 - Prob. 16ECh. 8.2 - In Problems 924, find the exact value of each...Ch. 8.2 - Prob. 18ECh. 8.2 - Prob. 19ECh. 8.2 - Prob. 20ECh. 8.2 - In Problems 924, find the exact value of each...Ch. 8.2 - Prob. 22ECh. 8.2 - Prob. 23ECh. 8.2 - Prob. 24ECh. 8.2 - Prob. 25ECh. 8.2 - Prob. 26ECh. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - Prob. 30ECh. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - Prob. 33ECh. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - Prob. 39ECh. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - In Problems 27-42, find the exact value of each...Ch. 8.2 - In Problems 4354, use a calculator in radian or...Ch. 8.2 - In Problems 4354, use a calculator in radian or...Ch. 8.2 - In Problems 4354, use a calculator in radian or...Ch. 8.2 - In Problems 4354, use a calculator in radian or...Ch. 8.2 - In Problems 4354, use a calculator in radian or...Ch. 8.2 - Prob. 48ECh. 8.2 - In Problems 4354, use a calculator in radian or...Ch. 8.2 - Prob. 50ECh. 8.2 - In Problems 4354, use a calculator in radian or...Ch. 8.2 - In Problems 4354, use a calculator in radian or...Ch. 8.2 - In Problems 4354, use a calculator in radian or...Ch. 8.2 - In Problems 4354, use a calculator in radian or...Ch. 8.2 - In Problems 5558, use a graphing calculator set in...Ch. 8.2 - In Problems 5558, use a graphing calculator set in...Ch. 8.2 - In Problems 5558, use a graphing calculator set in...Ch. 8.2 - In Problems 5558, use a graphing calculator set in...Ch. 8.2 - Find the domain of the tangent function.Ch. 8.2 - Find the domain of the cotangent function.Ch. 8.2 - Find the domain of the secant function.Ch. 8.2 - Prob. 62ECh. 8.2 - Explain why the range of the cosecant function is...Ch. 8.2 - Explain why the range of the secant function is...Ch. 8.2 - Explain why the range of the cotangent function is...Ch. 8.2 - Explain why the range of the tangent function is...Ch. 8.2 - Seasonal business cycle. Suppose that profits on...Ch. 8.2 - Seasonal business cycle. Revenues from sales of a...Ch. 8.2 - Prob. 69ECh. 8.2 - Pollution. In a large city, the amount of sulfur...Ch. 8.2 - Prob. 71ECh. 8.3 - Find each of the following derivatives:...Ch. 8.3 - Find the slope of the graph of f(x) = cos x at...Ch. 8.3 - Find ddxcscx.Ch. 8.3 - Suppose that revenues from the sale of ski jackets...Ch. 8.3 - Prob. 1EDCh. 8.3 - In Problems 14, by inspecting a graph of y = sin x...Ch. 8.3 - In Problems 14, by inspecting a graph of y = sin x...Ch. 8.3 - In Problems 14, by inspecting a graph of y = sin x...Ch. 8.3 - Prob. 4ECh. 8.3 - Prob. 5ECh. 8.3 - In Problems 58, by inspecting a graph of y = sin x...Ch. 8.3 - In Problems 58, by inspecting a graph of y = sin x...Ch. 8.3 - In Problems 58, by inspecting a graph of y = sin x...Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Prob. 22ECh. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Find the indicated derivatives in Problems 926....Ch. 8.3 - Prob. 26ECh. 8.3 - Find the slope of the graph of f(x) = sin x at x =...Ch. 8.3 - Find the slope of the graph of f(x) = cos x at x =...Ch. 8.3 - Prob. 29ECh. 8.3 - From the graph of y = f'(x) on the next page,...Ch. 8.3 - Prob. 31ECh. 8.3 - Find the indicated derivatives in Problems 3138....Ch. 8.3 - Find the indicated derivatives in Problems 3138....Ch. 8.3 - Find the indicated derivatives in Problems 3138....Ch. 8.3 - Find the indicated derivatives in Problems 3138....Ch. 8.3 - Find the indicated derivatives in Problems 3138....Ch. 8.3 - Find the indicated derivatives in Problems 3138....Ch. 8.3 - Find the indicated derivatives in Problems 3138....Ch. 8.3 - In Problems 39 and 40, find f(x). 39.f(x) = ex sin...Ch. 8.3 - Prob. 40ECh. 8.3 - In Problems 4146, graph each function on a...Ch. 8.3 - In Problems 4146, graph each function on a...Ch. 8.3 - Prob. 43ECh. 8.3 - In Problems 4146, graph each function on a...Ch. 8.3 - In Problems 4146, graph each function on a...Ch. 8.3 - In Problems 4146, graph each function on a...Ch. 8.3 - Profit. Suppose that profits on the sale of...Ch. 8.3 - Revenue. Revenues from sales of a soft drink over...Ch. 8.3 - Physiology. A normal seated adult inhales and...Ch. 8.3 - Pollution. In a large city, the amount of sulfur...Ch. 8.4 - Find the area under the cosine curve y = cos x...Ch. 8.4 - Find cos20tdt.Ch. 8.4 - Find sinxcosxdx.Ch. 8.4 - Prob. 4MPCh. 8.4 - Suppose that revenues from the sale of ski jackets...Ch. 8.4 - Prob. 1ECh. 8.4 - In Problems 18, by using only the unit circle...Ch. 8.4 - In Problems 18, by using only the unit circle...Ch. 8.4 - In Problems 18, by using only the unit circle...Ch. 8.4 - In Problems 18, by using only the unit circle...Ch. 8.4 - In Problems 18, by using only the unit circle...Ch. 8.4 - In Problems 18, by using only the unit circle...Ch. 8.4 - Prob. 8ECh. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Prob. 13ECh. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Prob. 18ECh. 8.4 - Evaluate each of the definite integrals in...Ch. 8.4 - Evaluate each of the definite integrals in...Ch. 8.4 - Evaluate each of the definite integrals in...Ch. 8.4 - Evaluate each of the definite integrals in...Ch. 8.4 - Find the shaded area under the cosine curve in the...Ch. 8.4 - Find the shaded area under the sine curve in the...Ch. 8.4 - Use a calculator to evaluate the definite...Ch. 8.4 - Prob. 26ECh. 8.4 - Use a calculator to evaluate the definite...Ch. 8.4 - Prob. 28ECh. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Find each of the indefinite integrals in Problems...Ch. 8.4 - Given the definite integral I=03exsinxdx (A)Graph...Ch. 8.4 - Given the definite integral I=03excosxdx (A)Graph...Ch. 8.4 - Seasonal business cycle. Suppose that profits on...Ch. 8.4 - Seasonal business cycle. Revenues from sales of a...Ch. 8.4 - Pollution. In a large city, the amount of sulfur...Ch. 8 - Convert to radian measure in terms of : (A) 30(B)...Ch. 8 - Evaluate without using a calculator: (A) cos (B)...Ch. 8 - In Problems 36, find each derivative or integral....Ch. 8 - In Problems 36, find each derivative or integral....Ch. 8 - Prob. 5RECh. 8 - In Problems 36, find each derivative or integral....Ch. 8 - Convert to degree measure: (A) /6(B) /4(C) /3(D)...Ch. 8 - Evaluate without using a calculator: (A) sin6(B)...Ch. 8 - Evaluate with the use of a calculator: (A) cos...Ch. 8 - Prob. 10RECh. 8 - Prob. 11RECh. 8 - In Problems 1218, find each derivative or...Ch. 8 - In Problems 1218, find each derivative or...Ch. 8 - In Problems 1218, find each derivative or...Ch. 8 - Prob. 15RECh. 8 - In Problems 1218, find each derivative or...Ch. 8 - Prob. 17RECh. 8 - In Problems 1218, find each derivative or...Ch. 8 - Prob. 19RECh. 8 - Find the area under the sine curve y = sin x from...Ch. 8 - Given the definite integral I=15sinxxdx (A)Graph...Ch. 8 - Convert 15 to radian measure.Ch. 8 - Evaluate without using a calculator: (A) sin32 (B)...Ch. 8 - Prob. 24RECh. 8 - In Problems 2428, find each derivative or...Ch. 8 - In Problems 2428, find each derivative or...Ch. 8 - In Problems 2428, find each derivative or...Ch. 8 - In Problems 2428, find each derivative or...Ch. 8 - In Problems 2931, graph each function on a...Ch. 8 - In Problems 2931, graph each function on a...Ch. 8 - In Problems 2931, graph each function on a...Ch. 8 - Prob. 32RECh. 8 - Prob. 33RECh. 8 - Prob. 34RECh. 8 - Prob. 35RE
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