EXPONENTIAL AND
LOGARITHMIC FUNCTIONS
3.1 & 3.2
EXPONENTIAL FUNCTIONS
  Exponential
functions have the form:
f(x) = ax
10
9
8
y1
7
0.0041
6
0.0123
5
0.037
4
0.1111
3
0.3333
2
1
1
3
9
-4
-3
-2
-1
-1
-2
1
2
3
4
27
81
LOGARITHMIC FUNCTIONS
(INVERSE OF THE EXPONENTIAL FUNCTIONS
WITH THE SAME BASE)
  Logarithmic
functions have the form:
f(x) = loga(x)
5
4
y1
3
2
-0.693
1
0
0.4055
-2
-1
-1
-2
-3
1
2
3
4
5
6
7
8
9
10
0.6931
0.9163
1.0986
1.2528
-4
-5
1.3863
1.5041
RECALL: FUNCTION TRANSFORMATIONS
f(x + a) moves the function “a” units to the left
f(x) + a moves the function “a” units up
f(-x) reflects the the graph about the y-axis
-f(x) reflects the graph about the x-axis
SIMPLE VS. COMPOUNDED INTEREST
Simple Interest
Compound Interest
Linear growth
(interest is only calculated from
the principal)
Exponential growth
(interest is calculated on both
previous interest and principal)
A formula for simple interest is:
A=P(1 + tr)
A formula for compound interest is:
⎛ r ⎞ nt
A = P⎜1+ ⎟
⎝ n ⎠
where A=amount after t years, P=principal amount, t= # of years,
n= # compoundings per year, and r=annual interest rate
€
If interest is compounded continuously this becomes:
A = Pert
APPLICATIONS
  Investments
  Loans
  Radioactive
  Population
Decay
Growth