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Unit 5: Exponential Functions (Logarithmic Functions (Inverse of y = 10^x,…
Unit 5: Exponential Functions
Logarithmic Functions
Inverse of y = 10^x, written as y = log10x
logba=c, b^c=a
Product of Logarithms Property: logbMN = logbM + logbN
Quotient of Logarithms Property: logbM/N = logbM - logbN
Power of Logarithms Property: logbM^P = PlogbM
Change of Base Property: all positive b, c not 1, logbM = (logcM)/(logcb)
Exponential Growth or Decay
Growth: y = ab^x, b>1, a not 0, Horizontal asymptote: y = 0
Decay: y = ab^x, 0<b<1, a not 0, Horizontal asymptote: y = 0
Fractional exponents: X^a/b is the b root of x^a
Inverse Functions
Definition: Two functions f and g are inverse functions if g(b)= a whenever f(a) = b
Horizontal line test: shows if a function is one-to-one and if it has an inverse
To find an inverse, reflect the function over the line y = x
The Number "e"
Compound interest formula: A = Ao(1+r/n)^nt
Ao = initial amount
r = annual interest rate (as dec.)
n = # of times compounded per year
t = time in years
"e" is the value of the compound interest formula as n gets infinitely large
compounding continuously: A = Pe^rt