Exponential Rules
(+ and -)
(+ and -)
Exponential Rules
(* or /)
(* or /)
Zero/Negative/Rational Exponents
Exponential Functions
Sequences
100
am * an
am+n
100
(am)n
am*n
100
a0
1
100
Exponential function formula
abx
100
What sequences increase or decrease by a consistent rate (+ or -)?
Artihmetic
200
am / an
am-n
200
(ab)x
ax * bx
200
a-n
1/an
200
What do a, b, and x stand for?
a - starting value, b - rate, x - iterations (how many weeks go by, years, days, etc.)
200
What sequences increase at a consistent rate (* or /)?
Geometric
300
x6 * x8
x14
300
(a/b)x
ax / bx
300
a1/n
nth root of a
300
Show me a graph of exponential growth!
300
Geometric Sequence Formula
an = a1 * rn-1 , n>0
400
y9 / y2
y7
400
(s3)6 * (rt2)2
r2 * s18 * t4
400
am/n
nth root of am
400
Show me a graph of exponential decay!
400
Sequence that uses prior term to determine the next term
Recursive sequence
500
(x4 * y3 * x2 * y7)/(y * x3 * y4)
x3 * y5
500
(t3)2 * (xy)2 / (wz)4
t6 (x2 * y2 ) / (w4 * z4)
500
s-2 * r0 * t2/3
1 * 1/s2 * cube root of t2
500
A new social media site is increasing its user base by approximately 6% per month. If the site currently has 21,740 users, what will the approximate user base be 8 months from now?
y=21,740(1.06)8
y= 34,650 users
500
What sequence is this?
0,1,1,2,3,5,8,13,21,34,55,89...
The Fibonacci Sequence!