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 9.3, Problem 15E
To determine
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f'(x)
A body of mass m at the top of a 100 m high tower is thrown vertically upward with an initial velocity of 10 m/s. Assume that the air resistance FD acting on the body is proportional to the velocity V, so that FD=kV. Taking g = 9.75 m/s2 and k/m = 5 s, determine: a) what height the body will reach at the top of the tower, b) how long it will take the body to touch the ground, and c) the velocity of the body when it touches the ground.
A chemical reaction involving the interaction of two substances A and B to form a new compound X is called a second order reaction. In such cases it is observed that the rate of reaction (or the rate at which the new compound is formed) is proportional to the product of the remaining amounts of the two original substances. If a molecule of A and a molecule of B combine to form a molecule of X (i.e., the reaction equation is A + B ⮕ X), then the differential equation describing this specific reaction can be expressed as:
dx/dt = k(a-x)(b-x)
where k is a positive constant, a and b are the initial concentrations of the reactants A and B, respectively, and x(t) is the concentration of the new compound at any time t. Assuming that no amount of compound X is present at the start, obtain a relationship for x(t). What happens when t ⮕∞?
Chapter 9 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.
Ch. 9.1 - Show that y=Cx+1 is the general solution of the...Ch. 9.1 - Prob. 2MPCh. 9.1 - Prob. 3MPCh. 9.1 - Prob. 4MPCh. 9.1 - Prob. 5MPCh. 9.1 - Prob. 1EDCh. 9.1 - Prob. 2EDCh. 9.1 - Prob. 1ECh. 9.1 - Prob. 2ECh. 9.1 - Prob. 3E
Ch. 9.1 - Prob. 4ECh. 9.1 - Prob. 5ECh. 9.1 - Prob. 6ECh. 9.1 - Prob. 7ECh. 9.1 - Prob. 8ECh. 9.1 - In Problems 110, find the derivative. (If...Ch. 9.1 - Prob. 10ECh. 9.1 - Prob. 11ECh. 9.1 - In Problems 1120, show that the given function is...Ch. 9.1 - Prob. 13ECh. 9.1 - Prob. 14ECh. 9.1 - Prob. 15ECh. 9.1 - Prob. 16ECh. 9.1 - Prob. 17ECh. 9.1 - Prob. 18ECh. 9.1 - Prob. 19ECh. 9.1 - Prob. 20ECh. 9.1 - Prob. 21ECh. 9.1 - In Problems 2124, determine which of the slope...Ch. 9.1 - In Problems 2124, determine which of the slope...Ch. 9.1 - Prob. 24ECh. 9.1 - Prob. 25ECh. 9.1 - In Problems 2528, use the appropriate slope...Ch. 9.1 - Prob. 27ECh. 9.1 - Prob. 28ECh. 9.1 - In Problems 2938, show that the given function y...Ch. 9.1 - Prob. 30ECh. 9.1 - Prob. 31ECh. 9.1 - In Problems 2938, show that the given function y...Ch. 9.1 - Prob. 33ECh. 9.1 - Prob. 34ECh. 9.1 - Prob. 35ECh. 9.1 - Prob. 36ECh. 9.1 - Prob. 37ECh. 9.1 - Prob. 38ECh. 9.1 - Prob. 39ECh. 9.1 - Prob. 40ECh. 9.1 - Prob. 41ECh. 9.1 - Prob. 42ECh. 9.1 - Prob. 43ECh. 9.1 - If y is defined implicitly by the given equation,...Ch. 9.1 - Prob. 45ECh. 9.1 - Prob. 46ECh. 9.1 - Prob. 47ECh. 9.1 - Prob. 48ECh. 9.1 - Prob. 49ECh. 9.1 - Prob. 50ECh. 9.1 - Prob. 51ECh. 9.1 - Prob. 52ECh. 9.1 - Prob. 53ECh. 9.1 - Prob. 54ECh. 9.1 - Prob. 55ECh. 9.1 - In Problems 55 and 56, use the general solution y...Ch. 9.1 - Prob. 57ECh. 9.1 - Prob. 58ECh. 9.1 - In Problems 59 and 60, use window dimensions Xmin...Ch. 9.1 - Prob. 60ECh. 9.1 - Prob. 61ECh. 9.1 - Prob. 62ECh. 9.1 - Prob. 63ECh. 9.1 - Prob. 64ECh. 9.1 - Prob. 65ECh. 9.1 - Prob. 66ECh. 9.1 - Rumor spreadGompertz growth model. The rate of...Ch. 9.2 - Solve: y=4x3y2.Ch. 9.2 - Prob. 2MPCh. 9.2 - Repeat Example 3 if the mothballs lose half their...Ch. 9.2 - Prob. 4MPCh. 9.2 - Prob. 5MPCh. 9.2 - Prob. 1EDCh. 9.2 - Prob. 2EDCh. 9.2 - Prob. 1ECh. 9.2 - Prob. 2ECh. 9.2 - Prob. 3ECh. 9.2 - Prob. 4ECh. 9.2 - Prob. 5ECh. 9.2 - In Problems 18, find the most general...Ch. 9.2 - Prob. 7ECh. 9.2 - Prob. 8ECh. 9.2 - Prob. 9ECh. 9.2 - In Problems 912, write a differential equation...Ch. 9.2 - In Problems 912, write a differential equation...Ch. 9.2 - Prob. 12ECh. 9.2 - Prob. 13ECh. 9.2 - Prob. 14ECh. 9.2 - Prob. 15ECh. 9.2 - Prob. 16ECh. 9.2 - Prob. 17ECh. 9.2 - Prob. 18ECh. 9.2 - Prob. 19ECh. 9.2 - Prob. 20ECh. 9.2 - Prob. 21ECh. 9.2 - In Problems 2130, find the general solution for...Ch. 9.2 - Prob. 23ECh. 9.2 - Prob. 24ECh. 9.2 - Prob. 25ECh. 9.2 - In Problems 2130, find the general solution for...Ch. 9.2 - Prob. 27ECh. 9.2 - Prob. 28ECh. 9.2 - In Problems 2130, find the general solution for...Ch. 9.2 - Prob. 30ECh. 9.2 - Prob. 31ECh. 9.2 - Prob. 32ECh. 9.2 - Prob. 33ECh. 9.2 - Prob. 34ECh. 9.2 - Prob. 35ECh. 9.2 - In Problems 3140, find the general solution for...Ch. 9.2 - Prob. 37ECh. 9.2 - Prob. 38ECh. 9.2 - Prob. 39ECh. 9.2 - In Problems 3140, find the general solution for...Ch. 9.2 - Prob. 41ECh. 9.2 - Prob. 42ECh. 9.2 - Prob. 43ECh. 9.2 - Prob. 44ECh. 9.2 - In Problems 4146, find the general solution for...Ch. 9.2 - Prob. 46ECh. 9.2 - Prob. 47ECh. 9.2 - Prob. 48ECh. 9.2 - Prob. 49ECh. 9.2 - Prob. 50ECh. 9.2 - Prob. 51ECh. 9.2 - Prob. 52ECh. 9.2 - Prob. 53ECh. 9.2 - Prob. 54ECh. 9.2 - Prob. 55ECh. 9.2 - Prob. 56ECh. 9.2 - Prob. 57ECh. 9.2 - Prob. 58ECh. 9.2 - Prob. 59ECh. 9.2 - Prob. 60ECh. 9.2 - Advertising. A company is using radio advertising...Ch. 9.2 - Prob. 62ECh. 9.2 - Prob. 63ECh. 9.2 - Prob. 64ECh. 9.2 - Prob. 65ECh. 9.2 - Prob. 66ECh. 9.2 - Prob. 67ECh. 9.2 - Prob. 68ECh. 9.2 - Prob. 69ECh. 9.2 - Prob. 70ECh. 9.2 - Prob. 71ECh. 9.2 - Prob. 72ECh. 9.2 - Newtons law of cooling states that the rate of...Ch. 9.2 - Prob. 74ECh. 9.2 - Population growth. A culture of bacteria is...Ch. 9.2 - Prob. 76ECh. 9.2 - Prob. 77ECh. 9.2 - Prob. 78ECh. 9.2 - Prob. 79ECh. 9.2 - Prob. 80ECh. 9.2 - Prob. 81ECh. 9.2 - Learning. The number of words per minute. N, a...Ch. 9.2 - Prob. 83ECh. 9.3 - Solve:xy+3y=4x.Ch. 9.3 - Prob. 2MPCh. 9.3 - Repeat Example 3 if the account earns 5%...Ch. 9.3 - If D = 70 + 2p(t) + 2p(t), S = 30 + 6p(t) + 3p(t)....Ch. 9.3 - Repeat Example 5 if water is released from the...Ch. 9.3 - Prob. 1EDCh. 9.3 - Prob. 2EDCh. 9.3 - Prob. 1ECh. 9.3 - Prob. 2ECh. 9.3 - Prob. 3ECh. 9.3 - Prob. 4ECh. 9.3 - Prob. 5ECh. 9.3 - Prob. 6ECh. 9.3 - Prob. 7ECh. 9.3 - Prob. 8ECh. 9.3 - Prob. 9ECh. 9.3 - Prob. 10ECh. 9.3 - Prob. 11ECh. 9.3 - Prob. 12ECh. 9.3 - Prob. 13ECh. 9.3 - Prob. 14ECh. 9.3 - Prob. 15ECh. 9.3 - Prob. 16ECh. 9.3 - Prob. 17ECh. 9.3 - Prob. 18ECh. 9.3 - Prob. 19ECh. 9.3 - Prob. 20ECh. 9.3 - Prob. 21ECh. 9.3 - Prob. 22ECh. 9.3 - Prob. 23ECh. 9.3 - In Problems 2334, find the integrating factor, the...Ch. 9.3 - Prob. 25ECh. 9.3 - In Problems 2334, find the integrating factor, the...Ch. 9.3 - Prob. 27ECh. 9.3 - Prob. 28ECh. 9.3 - In Problems 2334, find the integrating factor, the...Ch. 9.3 - Prob. 30ECh. 9.3 - Prob. 31ECh. 9.3 - Prob. 32ECh. 9.3 - Prob. 33ECh. 9.3 - In Problems 2334, find the integrating factor, the...Ch. 9.3 - Prob. 35ECh. 9.3 - Prob. 36ECh. 9.3 - Prob. 37ECh. 9.3 - Prob. 38ECh. 9.3 - In Problems 3514, find the integrating factor fix...Ch. 9.3 - In Problems 3514, find the integrating factor fix...Ch. 9.3 - Prob. 41ECh. 9.3 - Prob. 42ECh. 9.3 - Prob. 43ECh. 9.3 - Prob. 44ECh. 9.3 - Prob. 45ECh. 9.3 - Prob. 46ECh. 9.3 - Prob. 47ECh. 9.3 - Prob. 48ECh. 9.3 - Prob. 49ECh. 9.3 - Prob. 50ECh. 9.3 - Prob. 51ECh. 9.3 - Prob. 52ECh. 9.3 - Prob. 53ECh. 9.3 - Prob. 54ECh. 9.3 - Prob. 55ECh. 9.3 - Prob. 56ECh. 9.3 - Prob. 57ECh. 9.3 - Prob. 58ECh. 9.3 - Prob. 59ECh. 9.3 - Prob. 60ECh. 9.3 - Prob. 61ECh. 9.3 - Prob. 62ECh. 9.3 - Prob. 63ECh. 9.3 - Prob. 64ECh. 9.3 - Prob. 65ECh. 9.3 - Prob. 66ECh. 9.3 - Supply-demand. The supply S and demand D for a...Ch. 9.3 - Prob. 68ECh. 9.3 - Pollution. A 1,000-gallon holding tank contains...Ch. 9.3 - Pollution. Rework Problem 69 if water is entering...Ch. 9.3 - Pollution. Rework Problem 69 if water is entering...Ch. 9.3 - Prob. 72ECh. 9.3 - Pollution. Refer to Problem 69. When will the tank...Ch. 9.3 - Prob. 74ECh. 9.3 - Prob. 75ECh. 9.3 - Prob. 76ECh. 9.3 - Prob. 77ECh. 9.3 - In an article in the College Mathematics Journal...Ch. 9.3 - Prob. 79ECh. 9.3 - In 1960, William K. Estes proposed the following...Ch. 9 - In Problems 1 and 2, show that the given function...Ch. 9 - In Problems 1 and 2, show that the given function...Ch. 9 - In Problems 3 and 4, determine which of the...Ch. 9 - In Problems 3 and 4, determine which of the...Ch. 9 - In Problems 5 and 6, use the appropriate slope...Ch. 9 - In Problems 5 and 6, use the appropriate slope...Ch. 9 - In Problems 7 and 8, write a differential equation...Ch. 9 - In Problems 7 and 8, write a differential equation...Ch. 9 - In Problems 9 and 10, describe in words the rate...Ch. 9 - In Problems 9 and 10, describe in words the rate...Ch. 9 - In Problems 1116, determine whether the...Ch. 9 - In Problems 1116, determine whether the...Ch. 9 - In Problems 1116, determine whether the...Ch. 9 - In Problems 1116, determine whether the...Ch. 9 - In Problems 1116, determine whether the...Ch. 9 - Prob. 16RECh. 9 - In Problems 1724, find the general solution....Ch. 9 - In Problems 1724, find the general solution....Ch. 9 - In Problems 1724, find the general solution....Ch. 9 - In Problems 1724, find the general solution....Ch. 9 - In Problems 1724, find the general solution....Ch. 9 - In Problems 1724, find the general solution....Ch. 9 - Prob. 23RECh. 9 - In Problems 1724, find the general solution....Ch. 9 - In Problems, 2532, find the particular solution...Ch. 9 - In Problems, 2532, find the particular solution...Ch. 9 - In Problems, 2532, find the particular solution...Ch. 9 - In Problems, 2532, find the particular solution...Ch. 9 - In Problems, 2532, find the particular solution...Ch. 9 - In Problems, 2532, find the particular solution...Ch. 9 - In Problems, 2532, find the particular solution...Ch. 9 - In Problems, 2532, find the particular solution...Ch. 9 - Solve the following differential equation two...Ch. 9 - Give an example of an equation that can be solved...Ch. 9 - Prob. 35RECh. 9 - Prob. 36RECh. 9 - Prob. 37RECh. 9 - Prob. 38RECh. 9 - Prob. 39RECh. 9 - Prob. 40RECh. 9 - Prob. 41RECh. 9 - Prob. 42RECh. 9 - Prob. 43RECh. 9 - Prob. 44RECh. 9 - Prob. 45RECh. 9 - Prob. 46RECh. 9 - Prob. 47RECh. 9 - Rumor spread. A single individual starts a rumor...
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