Precalculus: Mathematics for Calculus - 6th Edition

6th Edition

ISBN: 9780840068071

Author: Stewart, James, Redlin, Lothar, Watson, Saleem

Publisher: Cengage Learning

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Textbook Question

Chapter 4.1, Problem 1E

The function f(x) = 5^x is an exponential function with base _____; f(−2) = _____, f(0) = _____, f(2) = _____, and f(6) = _____.

Expert Solution & Answer

To determine

To Evaluate: The base of an exponential function $f(x)=5x$ and the value for the function $f(−2), f(0), f(2) and f(6)$ .

Answer to Problem 1E

The base of an exponential function $f(x)=5x$ is 5 and the value of the function $f(−2)$ is $125$ , $f(0)$ is 1, $f(2)$ is 25 and $f(6)$ is 15,625.

Explanation of Solution

The exponential expression of a function is, $f(x)=ax$ .

Where,

a is base of the function.
x is any real number.

The given equation of the exponential function is, $f(x)=5x$ .

So, the base of the above function is 5.

Hence, the function $f(x)=5x$ is an exponential function with base 5.

The given equation of the exponential function is, $f(x)=5x$ .

Substitute $−2$ for x in the above equation,

$f(−2)=5−2f(−2)=152f(−2)=125$

Hence, the value of the exponential function $f(−2)$ is $125$ .

Substitute 0 for x in the above equation,

$f(0)=50f(0)=1$

Hence, the value of the exponential function $f(0)$ is 1.

Substitute 2 for x in the above equation,

$f(2)=52f(2)=25$

Hence, the value of the exponential function $f(2)$ is 25.

Substitute 6 for x in the above equation,

$f(6)=56f(6)=15625$

Hence, the value of the exponential function $f(6)$ is 15,625.

Chapter 3, Problem 6P

Chapter 4.1, Problem 2E

Chapter 4 Solutions

Precalculus: Mathematics for Calculus - 6th Edition

Ch. 4.1 - The function f(x) = 5x is an exponential function...Ch. 4.1 - Prob. 2E Ch. 4.1 - (a) To obtain the graph of g(x) = 2x 1, we start...Ch. 4.1 - In the formula A(t)=P(1+rn)nt for compound...Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E

Ch. 4.1 - Prob. 11E Ch. 4.1 - Prob. 12E Ch. 4.1 - Prob. 13E Ch. 4.1 - Prob. 14E Ch. 4.1 - Prob. 15E Ch. 4.1 - Prob. 16E Ch. 4.1 - Prob. 17E Ch. 4.1 - Prob. 18E Ch. 4.1 - Prob. 19E Ch. 4.1 - Prob. 20E Ch. 4.1 - Prob. 21E Ch. 4.1 - Prob. 22E Ch. 4.1 - Prob. 23E Ch. 4.1 - Prob. 24E Ch. 4.1 - Prob. 25E Ch. 4.1 - Prob. 26E Ch. 4.1 - Prob. 27E Ch. 4.1 - Prob. 28E Ch. 4.1 - Prob. 29E Ch. 4.1 - Prob. 30E Ch. 4.1 - Prob. 31E Ch. 4.1 - Prob. 32E Ch. 4.1 - Prob. 33E Ch. 4.1 - Prob. 34E Ch. 4.1 - Prob. 35E Ch. 4.1 - Prob. 36E Ch. 4.1 - Prob. 37E Ch. 4.1 - Prob. 38E Ch. 4.1 - Prob. 39E Ch. 4.1 - Prob. 40E Ch. 4.1 - Prob. 41E Ch. 4.1 - Prob. 42E Ch. 4.1 - Prob. 43E Ch. 4.1 - Prob. 44E Ch. 4.1 - Prob. 45E Ch. 4.1 - Prob. 46E Ch. 4.1 - Prob. 47E Ch. 4.1 - Prob. 48E Ch. 4.1 - Prob. 49E Ch. 4.1 - Prob. 50E Ch. 4.1 - Compound Interest If 10,000 is invested at an...Ch. 4.1 - Compound Interest If 2500 is invested at an...Ch. 4.1 - Compound Interest If 500 is invested at an...Ch. 4.1 - Compound Interest If 4000 is borrowed at a rate of...Ch. 4.1 - Present Value The present value of a sum of money...Ch. 4.1 - Present Value The present value of a sum of money...Ch. 4.1 - Prob. 57E Ch. 4.1 - Prob. 58E Ch. 4.1 - Prob. 59E Ch. 4.1 - Prob. 60E Ch. 4.2 - The function f(x) = ex is called the __________...Ch. 4.2 - In the formula A(t) = Pert for continuously...Ch. 4.2 - Prob. 3E Ch. 4.2 - Prob. 4E Ch. 4.2 - Prob. 5E Ch. 4.2 - Prob. 6E Ch. 4.2 - Prob. 7E Ch. 4.2 - Prob. 8E Ch. 4.2 - Prob. 9E Ch. 4.2 - Prob. 10E Ch. 4.2 - Prob. 11E Ch. 4.2 - Prob. 12E Ch. 4.2 - Prob. 13E Ch. 4.2 - Prob. 14E Ch. 4.2 - Prob. 15E Ch. 4.2 - Prob. 16E Ch. 4.2 - Prob. 17E Ch. 4.2 - Prob. 18E Ch. 4.2 - Prob. 19E Ch. 4.2 - Prob. 20E Ch. 4.2 - Prob. 21E Ch. 4.2 - Prob. 22E Ch. 4.2 - Sky Diving A sky diver jumps from a reasonable...Ch. 4.2 - Mixtures and Concentrations A 50-gal barrel is...Ch. 4.2 - Logistic Growth Animal populations are not capable...Ch. 4.2 - Bird Population The population of a certain...Ch. 4.2 - World Population The relative growth rate of world...Ch. 4.2 - Tree Diameter For a certain type of tree the...Ch. 4.2 - Prob. 29E Ch. 4.2 - Compound Interest An investment of 7000 is...Ch. 4.2 - Compound Interest If 2000 is invested at an...Ch. 4.2 - Compound Interest If 3500 is invested at an...Ch. 4.2 - Compound Interest If 600 is invested at an...Ch. 4.2 - Prob. 34E Ch. 4.2 - Compound Interest Which of the given interest...Ch. 4.2 - Prob. 36E Ch. 4.2 - Investment A sum of 5000 is invested at an...Ch. 4.2 - Prob. 38E Ch. 4.3 - log x is the exponent to which the base 10 must be...Ch. 4.3 - The function f(x) = log9 x is the logarithm...Ch. 4.3 - Prob. 3E Ch. 4.3 - Match the logarithmic function with its graph. (a)...Ch. 4.3 - Prob. 5E Ch. 4.3 - Prob. 6E Ch. 4.3 - Prob. 7E Ch. 4.3 - Prob. 8E Ch. 4.3 - Prob. 9E Ch. 4.3 - Prob. 10E Ch. 4.3 - Prob. 11E Ch. 4.3 - Prob. 12E Ch. 4.3 - Prob. 13E Ch. 4.3 - Prob. 14E Ch. 4.3 - Prob. 15E Ch. 4.3 - Prob. 16E Ch. 4.3 - Prob. 17E Ch. 4.3 - Prob. 18E Ch. 4.3 - Prob. 19E Ch. 4.3 - Prob. 20E Ch. 4.3 - Prob. 21E Ch. 4.3 - Prob. 22E Ch. 4.3 - Prob. 23E Ch. 4.3 - Prob. 24E Ch. 4.3 - Prob. 25E Ch. 4.3 - Prob. 26E Ch. 4.3 - Prob. 27E Ch. 4.3 - Prob. 28E Ch. 4.3 - Prob. 29E Ch. 4.3 - Prob. 30E Ch. 4.3 - Prob. 31E Ch. 4.3 - Prob. 32E Ch. 4.3 - Prob. 33E Ch. 4.3 - Prob. 34E Ch. 4.3 - Prob. 35E Ch. 4.3 - Prob. 36E Ch. 4.3 - Prob. 37E Ch. 4.3 - Prob. 38E Ch. 4.3 - Prob. 39E Ch. 4.3 - Prob. 40E Ch. 4.3 - Prob. 41E Ch. 4.3 - Prob. 42E Ch. 4.3 - Prob. 43E Ch. 4.3 - Prob. 44E Ch. 4.3 - Prob. 45E Ch. 4.3 - Prob. 46E Ch. 4.3 - Prob. 47E Ch. 4.3 - Prob. 48E Ch. 4.3 - Prob. 49E Ch. 4.3 - Prob. 50E Ch. 4.3 - Prob. 51E Ch. 4.3 - Prob. 52E Ch. 4.3 - Prob. 53E Ch. 4.3 - Prob. 54E Ch. 4.3 - Prob. 55E Ch. 4.3 - Prob. 56E Ch. 4.3 - Prob. 57E Ch. 4.3 - Prob. 58E Ch. 4.3 - Prob. 59E Ch. 4.3 - Prob. 60E Ch. 4.3 - Prob. 61E Ch. 4.3 - Prob. 62E Ch. 4.3 - Prob. 63E Ch. 4.3 - Prob. 64E Ch. 4.3 - Prob. 65E Ch. 4.3 - Prob. 66E Ch. 4.3 - Prob. 67E Ch. 4.3 - Prob. 68E Ch. 4.3 - Prob. 69E Ch. 4.3 - Prob. 70E Ch. 4.3 - Prob. 71E Ch. 4.3 - Prob. 72E Ch. 4.3 - Prob. 73E Ch. 4.3 - Prob. 74E Ch. 4.3 - Prob. 75E Ch. 4.3 - Prob. 76E Ch. 4.3 - Prob. 77E Ch. 4.3 - Prob. 78E Ch. 4.3 - Prob. 79E Ch. 4.3 - Prob. 80E Ch. 4.3 - Prob. 81E Ch. 4.3 - Prob. 82E Ch. 4.3 - Prob. 83E Ch. 4.3 - Prob. 84E Ch. 4.3 - Prob. 85E Ch. 4.3 - Absorption of Light A spectrophotometer measures...Ch. 4.3 - Carbon Dating The age of an ancient artifact can...Ch. 4.3 - Bacteria Colony A certain strain of bacteria...Ch. 4.3 - Prob. 89E Ch. 4.3 - Charging a Battery The rate at which a battery...Ch. 4.3 - Prob. 91E Ch. 4.3 - Prob. 92E Ch. 4.3 - Prob. 93E Ch. 4.3 - Prob. 94E Ch. 4.3 - Prob. 95E Ch. 4.4 - The logarithm of a product of two numbers is the...Ch. 4.4 - The logarithm of a quotient of two numbers is the...Ch. 4.4 - The logarithm of a number raised to a power is the...Ch. 4.4 - Prob. 4E Ch. 4.4 - Prob. 5E Ch. 4.4 - Prob. 6E Ch. 4.4 - Prob. 7E Ch. 4.4 - Prob. 8E Ch. 4.4 - Prob. 9E Ch. 4.4 - Prob. 10E Ch. 4.4 - Prob. 11E Ch. 4.4 - Prob. 12E Ch. 4.4 - Prob. 13E Ch. 4.4 - Prob. 14E Ch. 4.4 - Prob. 15E Ch. 4.4 - Prob. 16E Ch. 4.4 - Prob. 17E Ch. 4.4 - Prob. 18E Ch. 4.4 - Prob. 19E Ch. 4.4 - Prob. 20E Ch. 4.4 - Prob. 21E Ch. 4.4 - Prob. 22E Ch. 4.4 - Prob. 23E Ch. 4.4 - Prob. 24E Ch. 4.4 - Prob. 25E Ch. 4.4 - Prob. 26E Ch. 4.4 - Prob. 27E Ch. 4.4 - Prob. 28E Ch. 4.4 - Prob. 29E Ch. 4.4 - Prob. 30E Ch. 4.4 - Prob. 31E Ch. 4.4 - Prob. 32E Ch. 4.4 - Prob. 33E Ch. 4.4 - Prob. 34E Ch. 4.4 - Prob. 35E Ch. 4.4 - Prob. 36E Ch. 4.4 - Prob. 37E Ch. 4.4 - Prob. 38E Ch. 4.4 - Prob. 39E Ch. 4.4 - Prob. 40E Ch. 4.4 - Prob. 41E Ch. 4.4 - Prob. 42E Ch. 4.4 - Prob. 43E Ch. 4.4 - Prob. 44E Ch. 4.4 - Prob. 45E Ch. 4.4 - Prob. 46E Ch. 4.4 - Prob. 47E Ch. 4.4 - Prob. 48E Ch. 4.4 - Prob. 49E Ch. 4.4 - Prob. 50E Ch. 4.4 - Prob. 51E Ch. 4.4 - Prob. 52E Ch. 4.4 - Prob. 53E Ch. 4.4 - Prob. 54E Ch. 4.4 - Prob. 55E Ch. 4.4 - Prob. 56E Ch. 4.4 - Prob. 57E Ch. 4.4 - Prob. 58E Ch. 4.4 - Prob. 59E Ch. 4.4 - Prob. 60E Ch. 4.4 - Prob. 61E Ch. 4.4 - Prob. 62E Ch. 4.4 - Prob. 63E Ch. 4.4 - Prob. 64E Ch. 4.4 - Prob. 65E Ch. 4.4 - Prob. 66E Ch. 4.4 - Prob. 67E Ch. 4.4 - Prob. 68E Ch. 4.4 - Wealth Distribution Vilfredo Pareto (18481923)...Ch. 4.4 - Biodiversity Some biologists model the number of...Ch. 4.4 - Magnitude of Stars The magnitude M of a star is a...Ch. 4.4 - Prob. 72E Ch. 4.4 - Prob. 73E Ch. 4.4 - Prob. 74E Ch. 4.5 - Lets solve the exponential equation 2ex = 50. 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Atmospheric Pressure Atmospheric pressure P (in...Ch. 4.5 - Cooling an Engine Suppose youre driving your car...Ch. 4.5 - Electric Circuits An electric circuit contains a...Ch. 4.5 - Learning Curve A learning curve is a graph of a...Ch. 4.5 - Prob. 89E Ch. 4.5 - Prob. 90E Ch. 4.5 - Prob. 91E Ch. 4.6 - Population Growth These exercises use the...Ch. 4.6 - Population Growth These exercises use the...Ch. 4.6 - Population Growth These exercises use the...Ch. 4.6 - Prob. 4E Ch. 4.6 - Prob. 5E Ch. 4.6 - Prob. 6E Ch. 4.6 - Prob. 7E Ch. 4.6 - Prob. 8E Ch. 4.6 - Prob. 9E Ch. 4.6 - Prob. 10E Ch. 4.6 - Prob. 11E Ch. 4.6 - Population Growth These exercises use the...Ch. 4.6 - Population Growth These exercises use the...Ch. 4.6 - Population Growth These exercises use the...Ch. 4.6 - Prob. 15E Ch. 4.6 - Prob. 16E Ch. 4.6 - Radioactive Radium The half-life of radium-226 is...Ch. 4.6 - Radioactive Cesium The half-life of cesium-137 is...Ch. 4.6 - Radioactive Strontium The half-life of...Ch. 4.6 - Radioactive Radium Radium-221 has a half-life of...Ch. 4.6 - Finding Half-Life If 250 mg of a radioactive...Ch. 4.6 - Radioactive Radon After 3 days a sample of...Ch. 4.6 - Carbon-14 Dating A wooden artifact from an ancient...Ch. 4.6 - Carbon-14 Dating The burial cloth of an Egyptian...Ch. 4.6 - Law of Cooling These exercises use Newtons Law of...Ch. 4.6 - Law of Cooling These exercises use Newtons Law of...Ch. 4.6 - Prob. 27E Ch. 4.6 - Prob. 28E Ch. 4.6 - Prob. 29E Ch. 4.6 - Prob. 30E Ch. 4.6 - Prob. 31E Ch. 4.6 - Prob. 32E Ch. 4.6 - Prob. 33E Ch. 4.6 - Prob. 34E Ch. 4.6 - Prob. 35E Ch. 4.6 - Prob. 36E Ch. 4.6 - Prob. 37E Ch. 4.6 - Prob. 38E Ch. 4.6 - Prob. 39E Ch. 4.6 - Prob. 40E Ch. 4.6 - Prob. 41E Ch. 4.6 - Prob. 42E Ch. 4.6 - Prob. 43E Ch. 4 - Prob. 1RCC Ch. 4 - Prob. 2RCC Ch. 4 - Prob. 3RCC Ch. 4 - Prob. 4RCC Ch. 4 - Prob. 5RCC Ch. 4 - Prob. 6RCC Ch. 4 - Prob. 7RCC Ch. 4 - Prob. 8RCC Ch. 4 - Prob. 9RCC Ch. 4 - Prob. 10RCC Ch. 4 - Prob. 11RCC Ch. 4 - Prob. 12RCC Ch. 4 - Prob. 1RE Ch. 4 - Prob. 2RE Ch. 4 - Prob. 3RE Ch. 4 - Prob. 4RE Ch. 4 - 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The function f ( x ) = 5 x is an exponential function with base _____; f (−2) = _____, f (0) = _____, f (2) = _____, and f (6) = _____.

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Answer to Problem 1E

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Chapter 4 Solutions

The function f ( x ) = 5 x is an exponential function with base ___; f (−2) = _, f (0) = _, f (2) = _, and f (6) = ___.