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Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 34

Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 34. A major complaint of professors teaching calculus is that students don't have the appropriate background to work through the calculus course successfully. This text is targeted directly at this underprepared audience. This is a single-variable (2-semester) calculus text that incorporates a conceptual re-introduction to key precalculus ideas throughout the exposition as appropriate. This is the ideal resource for those schools dealing with poorly prepared students or for schools introducing a slower paced, integrated precalculus/calculus course | 9.2 Exponential The Bare Bones 311 Exponentiation does not distribute over addition or subtraction. Enough parentheses must be used when entering an exponential into your calculator or computer so that the typed expression is interpreted as you intended. These points are illustrated below. be2 bee be 2 e.g. for x 0 x2 is negative while x 2 is positive. ab n a lb l e.g. 2x 2 2 2 x2 4x2 2x2 2x2 a n _an 4 _ 4 x 2 _ 41 2 _ 2 b e gy 3 3 3 à1 2 73 But a b n an bn e.g. 2 3 2 52 25 but22 32 4 9 13. a b n an bn e.g. 725 9 25 9 1 2 161 2 4 but251 2 91 2 5 3 2. Entering 70S 00 i g 0 in a calculator gives 2x5 72 not 2x5 2 or 2x 5 2. To enter 2x 5 2 you can type 0 000 7 0 0. Different calculators may have slightly different conventions. Check yours out either by using the instruction manual or by playing around with numbers you know. Rounding off the bases of exponentials can cause substantial inaccuracy. Let your calculator work for you do not round off early. EXERCISE 9.2 Use a calculator or computer to evaluate the following to two decimal places. a n3 1 3 5 3 b 1 1 i 5 12 6 3. 1 3 1 33 c . 1 Answer a 1545 .1 b 1996. 7 c 56.73 EXERCISE 9.3 Each statement that follows is incorrect. Find the incorrect step and correct it. 312 CHAPTER 9 Exponential Functions i ii iii iv v x 8. 8 x 1 x-2 3 2 B3C-1 - 3 B2C-1 - 3 B-6C3 2 -3C3 C3 I 2B y 2 I 2 -3 B6 8B6 4x2 16y2 4 x2 4y2 V x2 4y2 2 x 2y 2x 4y A C _ A D C B _ AD CB _ AD CB V B D B D BD Bd V I V 2 I V 2 x y 2x 2y 2 x y x y Answers are provided at the end of the chapter. EXERCISE 9.4 Simplify the following. VWx3 1 2 . r- r G764x3 1 2 e3S Q 1 0 _1 2 ii 4 9y 1 iii iv x_2 v A2s 2x 1 2 bx A 2 Q2K 1 2 Answers are provided at the end of the chapter. The Exponential Function The function f is called an exponential function if it can be written in the form f Cb where C is a constant and b is a positive constant. This function is called exponential because the variable is in the exponent. The domain of the exponential function is all real .