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Section 3.1A

# Section 3.1A - x x x 1 10 50 100 1000 4 Applications –...

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1 Warm-up Section 3.1A x x x x x y y y y y - - = - = - = = = 2 ) 2 ( 3 2 2 2 1 x a x f = ) ( 1 a Exponential functions are functions of the form where x is any real number and a >0 and .

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2 What transformation results from each? ) ( ) ( x f y x f y - = - = Characteristics of an exponential function in the form y = a x . y = a x , a >1, x >0 y = a -x , a >1, x>0 The graph is continuous. The graph is continuous. Domain: Domain: Range: Range: As x→ +∞, y→ As x→ +∞, y→ As x→ -∞, y→ As x→ -∞, y→ Intercepts: Intercepts: Asymptote: Asymptote:
3 Recall the number e is a constant and is known as the natural base. The value of e is approximately ___________. As x gets very large the expression e x x + 1 1 ? 1 1

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Unformatted text preview: + x x x 1 10 50 100 1000 4 Applications – Compound Interest • After t years, the balance A in an account with principal P and annual interest rate r is given by the following formulas • For n compoundings per year: • • For continuous compounding: nt n r P A + = 1 rt Pe A = 5 Examples A total of \$12000 is invested at an annual interest rate of 3.5%. Find the balance after 5 years, if interest is compounded a. quarterly b. monthly c. continuously 6 7 Examples • Solve graphically ( 29 x x x x b a 2 05 . 1 3 2 . 3 1 2 .--=...
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Section 3.1A - x x x 1 10 50 100 1000 4 Applications –...

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