Pre-Calculus 12: Exponential and Logarithmic Functions

Basic exponential function

Form: y = c^x

• Major points (-1, 1/c) (1, c) and (0,1)

• Domain x(all real numbers), Range y>0 (untransformed)

i) Increasing/growing exponential (c>1)

ii) Decreasing/decaying exponential (0<c<1)

A=A_ok^bx

A = Final amount

Ao= initial amount

x = usually time or unit of measure

b= adjustment factor → 1 cycle/number of time per cycle

k = growth factor

• k=2 doubling

• k =1/2 half-life

• k= 1.04 → 4% increase

• k= 0.93 → 7% decrease

Transformation of exponential functions

y = a(c)^b(x-h)+K

• Remember the major points of the basic exponential function

• Horizontal asymptote is affected by vertical translation “k” value

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