Ebook College algebra (3rd edition): Part 2
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Ebook College algebra (3rd edition): Part 2
Exponential and jg?Logarithmic Functions^®chapter 4You've recently taken up weightlifting, recording the maximum number of pounds you can lift at the Ebook College algebra (3rd edition): Part 2 end of each week. At first your weight limit increases rapidly, but now you notice that this growth is beginning to level off. YOU wonder about a function that would serve as a mathematical model to predict the number of pounds you can lift us you continue the sport.What went wrong on the space shu Ebook College algebra (3rd edition): Part 2 ttle Chuilcn^ri Will population growth lead to a future without comfort or individual choice? Can I put aside a small amount of money and have millionEbook College algebra (3rd edition): Part 2
s for early rclữcmcnt? Why did I feel J was walking too slowly on my visit to New York City ? Why are people in California al far greater risk from drExponential and jg?Logarithmic Functions^®chapter 4You've recently taken up weightlifting, recording the maximum number of pounds you can lift at the Ebook College algebra (3rd edition): Part 2 sh in weightlifting?The functions that you will be learning about in this chapter will provide you with the mathematics for answering these questions. You will sec how these remarkable functions enable US to predict the future and rediscover the past.373374 • Chapter 4 • Exponential and Logarithmic Ebook College algebra (3rd edition): Part 2 FunctionsSECTION 4.1 Exponential FunctionsObjectives1.Evaluate exponential functions.2.Graph exponential functions.3.Evaluate functions with base e.4.Ebook College algebra (3rd edition): Part 2
Use compound interest formulas.The space shuttle Challenger exploded approximately 73 seconds into flight on January 28,1986. ’Ihe tragedy involved daExponential and jg?Logarithmic Functions^®chapter 4You've recently taken up weightlifting, recording the maximum number of pounds you can lift at the Ebook College algebra (3rd edition): Part 2 amatically as temperature falls.Ihe functionf(x) = 13.49(0.967)* - 1models the number of O-rings expected to fail when the temperature is X 'F. Can you see how this function is different from polynomial functions? The variable X is in the exponent. Functions whose equations contain a variable in the Ebook College algebra (3rd edition): Part 2 exponent are called exponential functions. Many real-life situations, including population growth, growth of epidemics, radioactive decay, and otherEbook College algebra (3rd edition): Part 2
changes that involve rapid increase or decrease, can be described using exponential functions.Definition of the Exponential FunctionThe exponential fuExponential and jg?Logarithmic Functions^®chapter 4You've recently taken up weightlifting, recording the maximum number of pounds you can lift at the Ebook College algebra (3rd edition): Part 2 rc some examples of exponential functions:M=2- six) = lữ" A(x)=3”>.ia 2.Base In 10.Bans is 3.Each of these functions has a constant base and a variable exponent. By contrast, the following functions are not exponential:F(x) - X‘G(x) = 1‘/7(x) = X*.Variable (0 the bane and not the exponent.The base o Ebook College algebra (3rd edition): Part 2 f an exponentialfriable la both function must ba a positive the base and the constant other than 1.exponent.Section 4.1 *a M.av.lKaaav ~ r Why is G(x)Ebook College algebra (3rd edition): Part 2
= r not classified as an exponential function? The number 1 raised to any power is l.Thus, the function G can be written as G’(j) = 1, which is a conExponential and jg?Logarithmic Functions^®chapter 4You've recently taken up weightlifting, recording the maximum number of pounds you can lift at the Ebook College algebra (3rd edition): Part 2 [ỹỊ key. Graphing calculators have a ỊÃ] key. To evaluate expressions oi the iorm bl. enter the base b. press [pi or [a], enter the exponent .V. and finally press [=) or IenterỊ. EXAMPLE 1 Evaluating an Exponential Function The exponential function f(x) = 13.49(0.967)' - 1 describes the number of O Ebook College algebra (3rd edition): Part 2 -rings expected to fail, f(x). when the temperature is X°F. On the morning the Challenger was launched, the temperature was 31°F, colder than any prevEbook College algebra (3rd edition): Part 2
ious experience. Find the number of O-rings expected to fail at this temperature. Solution Because the temperature was 31°F. substitute 31 for X and eExponential and jg?Logarithmic Functions^®chapter 4You've recently taken up weightlifting, recording the maximum number of pounds you can lift at the Ebook College algebra (3rd edition): Part 2 lculator to evaluate /(31). Press the following keys on your calculator to do this: Scientific calculator: 13.49 [3.967 rpl 311 ~ ‘ 1ẸỊ Graphing calculator: 13.49 13 -967 0 313 1 lENTrRl- The display should be approximately 3.7668627. /(31) = 13.49(0.967)" - 1 « 3.8 = 4 Thus, four O-rings are expect Ebook College algebra (3rd edition): Part 2 ed to fail at a temperature of 31 °F. Check Gse the function in Example 1 to find the number of O rings expected Point to fail at a temperature of 60°Ebook College algebra (3rd edition): Part 2
F. Round to the nearest whole number.-y Graph exponential JW functions.Graphing Exponential Functions We are familiar with expressions involving //, wExponential and jg?Logarithmic Functions^®chapter 4You've recently taken up weightlifting, recording the maximum number of pounds you can lift at the Ebook College algebra (3rd edition): Part 2 omain X. You may wonder what h' means when X is an irrational number, such as b''- or b". Using closer and closer approximations for V3 (V3 = 1.73205), we can think of as the value that has the successively closer approximations 61-’,/)«•», In this way. we can graph the exponential function with no Ebook College algebra (3rd edition): Part 2 holes, or points of discontinuity, at the irrational domain values.376 • Chapter 4 • Exponential and Logarithmic FunctionsEXAMPLE 2 Graphing an ExponeEbook College algebra (3rd edition): Part 2
ntial FunctionGraph: /(x) = 2‘.Exponential and jg?Logarithmic Functions^®chapter 4You've recently taken up weightlifting, recording the maximum number of pounds you can lift at the Exponential and jg?Logarithmic Functions^®chapter 4You've recently taken up weightlifting, recording the maximum number of pounds you can lift at theGọi ngay
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