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Calculus I (MAT 145) Dr. Day Wednesday Jan 23, 2013

Calculus I (MAT 145) Dr. Day Wednesday Jan 23, 2013. Collect Take-Home Assignment #1 Exponential Functions (1.5) Inverse Functions and Logarithmic Functions (1.6) Quiz #3 Assignments. Exponential Functions (PIP page 9; Text section 1.5). Exponential functions are of the form where.

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Calculus I (MAT 145) Dr. Day Wednesday Jan 23, 2013

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  1. Calculus I (MAT 145)Dr. Day Wednesday Jan 23, 2013 • Collect Take-Home Assignment #1 • Exponential Functions (1.5) • Inverse Functions and Logarithmic Functions (1.6) • Quiz #3 • Assignments MAT 145

  2. Exponential Functions(PIP page 9; Text section 1.5) Exponential functions are of the form where The input variable, the exponent, can be any real number. The base must be a positive real number. Why make this restriction? MAT 145

  3. Use and Apply Exponential Functions (1) The graph of contains the points (1,6) and (4,162). Determine C and a. (2) Some versions of biological warfare involve releasing highly effective fast-growing toxins into the atmosphere. Suppose that a toxin enters my body at 12 noon with an initial count of 20 bacteria cells. The cells double every 15 minutes. (a) If growth occurs as described above, and goes unchecked, represent the number of bacteria cells P in my body t hours after entering my body. (b) At what time will there be 1 million bacteria cells present? (3) A certain radio-active element has a half-life of 60 days. Suppose there are 8.5 grams present today, January 23, 2013. (a) If decay occurs as described above, represent the amount A, in grams, of the element that is present t days from now. (b) On what date (day, month, year) will there first be less than 2 grams present? MAT 145

  4. Functions and Their Inverses(PIP p 10-11; Text section 1.6) • Representing the inverse of a relationship. • Graphs, tables, symbols: f(x) = 5x – 2; g(x) = (4x + 3)/(x-2) • Does a function have an inverse that also is a function? • One-to-one functions • Inverses of exponential functions: Logarithmic functions MAT 145

  5. Logarithmic Functions • Inverses of exponential functions: Logarithmic functions exponent: y base: a MAT 145

  6. Assignments • WebAssign • Section 1.5 due tomorrow night • Section 1.6 due Friday night • Test #1: Monday, Jan 28; practice test available • Email MAT 145

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