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Rational and Exponential Functions

1 Growth factor of an exponential
function: growth factor is greater than 1

2 Exponential growth function: the quantity
increases, slowly at first, and then very rapidly.
The rate of change increases over time. The
rate of growth becomes faster as time passes.

3 Rational function: is any function which
can be defined by a rational fraction

4 Horizontal & Vertical Asymptotes of Rational Functions: Vertical
asymptotes are vertical lines which correspond to the zeroes of the
denominator of a rational function.

5 Initial amount for an exponential
function: starting amount before
the rate

6 Exponential decay function: the
quantity decreases very rapidly at first,
and then more slowly. The rate of
change decreases over time.

7 Decay factor of an exponential
function: the decay factor is 0 < b <
1

8 Horizontal Asymptotes of Exponential Functions

9 End behavior of a graph with asymptotes: for
numerically large values of x, we can sometimes
model the behavior of a complicated function by a
simpler one that acts virtually in the same way

10 Y-intercept of an exponential function

11 Exponential function: f (x) = abx

12 Compound Interest Formula: A=P(1+r/n)nt

13 Continuous Compounding: the process of
earning interest on top of interest. The
interest is earned constantly, and
immediately begins earning interest on
itself.

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