6.3 Exponential FunctionsKEY

6.3 Exponential FunctionsKEY - 6-3: Exponential Functions...

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Unformatted text preview: 6-3: Exponential Functions Exponential function is a function in the form f(x) = ax where a is a positive real number and a ≠ 1. The domain of f is the set of all real numbers. The laws of exponents for real (irrational) exponents are the same as those for integer and rational exponents. Irrational exponents are F+ 1 I 1 truncated to a finite number of digits, so that ar≈ ax. The number e is the number that G n J HK approaches as n→∞. n f(x) = ax Range x-intercept y-intercept a>1 (0, ∞ ) None (0, 1) Horizontal asymptote x-axis as x →-∞ 0<a<1 (0, ∞ ) None (0, 1) x-axis as x →∞ Characteristic Increasing, one-to-one Decreasing one-to-one Passes through (0, 1) (1, a) (0, 1) (1, a) Approximate to three decimal places: 1. 5 3 ≈ 16.242 2. 2e ≈ 6.581 Graph the following exponential functions; state the domain, range, and any horizontal asymptote: 3. x y=2 y = 2x+2; y = 2x – 2 1 FI y= G =2 HJ 2K x 4. -x 5. y = ex y = 2-x-2; y = -ex; y = 2-x + 2 y = 2 - ex 6. Atmospheric pressure p measured in mm of mercury is related to the number of km h above sea level by the formula p = 760e-0.145h. Find the pressure at a height of 2 km and at a height of 10 km. p =760e-0.145(2) ≈ 568.68 p =760e-0.145(10) ≈ 178.27 Exponential Equations: If au = av, then u = v. 1− 2 x 7. 5 1 = 5 1 8. 2 1− x =4 9. () e4 x 2 ⋅ e x = e 12 ...
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This note was uploaded on 01/04/2012 for the course MAC 1105 taught by Professor Staff during the Fall '08 term at Miami Dade College, Miami.

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