Textbook Question
In Exercises 1–4, the graph of an exponential function is given. Select the function for each graph from the following options: f(x) = 4^x, g(x) = 4^-x, h(x) = -4^(-x), r(x) = -4^(-x)+3 1.
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Ch. 4 - Exponential and Logarithmic Functions
Chapter 5, Problem 1
In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. 2^3.4
Verified Solution
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Exponents
Exponents represent repeated multiplication of a number by itself. In the expression 2^3.4, the base is 2, and the exponent is 3.4, indicating that 2 is multiplied by itself 3.4 times. Understanding how to manipulate exponents is crucial for evaluating expressions involving powers.
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Calculator Functions
Using a calculator effectively requires familiarity with its functions, especially for operations involving exponents. Most scientific calculators have a specific button for exponentiation, allowing users to input both the base and the exponent directly. Knowing how to round results to a specified number of decimal places is also essential for accuracy.
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Rounding Numbers
Rounding is the process of adjusting a number to a specified degree of accuracy, often to make it simpler or more understandable. In this case, rounding to three decimal places means keeping three digits after the decimal point and adjusting the last digit based on the value of the next digit. This concept is important for presenting numerical results clearly and concisely.
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Related Practice
Textbook Question
In Exercises 1–8, write each equation in its equivalent exponential form. 4 = log₂ 16
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Textbook Question
In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.
log5 (7 × 3)
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Textbook Question
Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 2^x=64
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