Algebra 3/ Trigonometry
Notes 4.1 Exponential Functions & their Graphs
𝑓(𝑥) = 𝑏 𝑥
ex.) 𝑦 = 2𝑥
ex.) 𝑦 = 2−𝑥
Compound Interest
 Simple Interest
Ex.)

𝐴 = 𝑃(1 + 𝑟) 𝑡
A=
P=
r=
t=
You invest $1000 in a bank’s certificate of deposit (CD) at 3% interest per year for 2 years.
How much is it worth after 2 years?
Periodic Compounding
𝑟
𝐴 = 𝑃(1 + 𝑛)𝑛 𝑡
n=
Ex.)
You invest $1000 in a bank’s certificate of deposit (CD) at 3% interest per year for 2 years
compounded monthly. How much is it worth after 2 years?
Ex.)
You invest $1000 in a bank’s certificate of deposit (CD) at 3% interest per year for 2 years
compounded weekly. How much is it worth after 2 years?

Continuous Compounding
𝐴 = 𝑃𝑒 𝑟 𝑡
As you can see, the computed value keeps getting larger and larger, the more often you compound. But
the growth is slowing down; as the number of compoundings increases, the computed value appears to
be approaching some fixed value. You might think that the value of the compound-interest formula is
getting closer and closer to a number that starts out "2.71828". And you'd be right; the number we're
approaching is called "e". This is known as Euler’s number or the “natural” exponential.
Ex.)
You invest $1000 in a bank’s certificate of deposit (CD) at 3% interest per year for 2 years
compounded continuously.
How much is it worth after 2 years?