Unit 9/10 Flashcards
Exponential Parent Function
y = ab^x
Exponential
The variable is an exponent. (Grows very fast, by the power)
If b > 1, exponential growth increasing
If b < 1, exponential decay decreaseing
Logarithmic Parent Function
The inverse of an exponential function
Logarithm
Another way of writing exponents .
logb a = x
b^x = a
Common logarithm
Has a base 10 and can be written without the base.
log10 x
e^x
If there is no subscript to log it is 10.
Change of base formula
logb a = (log a) / (log b)
b = base
e
An irrational number that is often the base of exponential and logarithmic functions that describe real world scenarios.
Base “e” exponential functions
Natural base exponential functions.
y = e^x
Base “e” logarithmic functions
Natural log exponential functions.
y = loge X OR y = lnX
Logarithmic regression
YEAR start X on 1. Anything else on 0.
Choosing the best regression model.
Look at the correlation ceofficient, r^2. Which ever one is closest to 1 is the best fit.
Sequence
A set of numbers with a particular order or pattern.
Each number called a term.
Term notation
First term in a sequence is a1.
n is the term number in the sequence.
Arithmetic sequence: Recursive formula
nth term = previous term of nth term plus common difference.
an = an-1 + d
Arithmetic sequence: Explicit formula
nth term = first term plus previous term of nth term times common difference.
an = a1 + (n-1)d
