4.1 Exponential Functions

# 4.1 Exponential Functions - MAC2233(3.4 North FIU MDC 4....

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MAC2233 (3.4) FIU, MDC- North 4.1 Exponential Functions Exponential Function:     f(x) = b x  (b > 0, b ≠ 1) for every real number  x .  For  b > 1 , f(x) is constantly increasing,  x x f x and f x lim ( ) 0, lim ( ) →-∞ →∞ = = +∞ .     For   0   <   b   <   1 ,   f(x)   is   constantly   decreasing,  x x f x and f x lim ( ) , lim ( ) 0 →-∞ →∞ = +∞ = .   [See your book for a review of definitions and basic properties of exponents.].   Compound Interest:    If   P  dollars are invested at an annual interest rate  r  (expressed as a decimal) and interest is  compounded  k  times a year, the  future value  (balance)  B(t)  after  t  years will be  kt r B P k 1 = + ÷ ; if it is compounded  continuously, the balance will be  rt B Pe = .  In order to have a given balance  B  in  t  years invested an annual rate  compounded   k   times a year, the Principal

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4.1 Exponential Functions - MAC2233(3.4 North FIU MDC 4....

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