Download Simple Interest Formula Compound Interest

Math 102
5.2 "Applications of Exponential Functions"
Objectives:
* Solve simple and compound interest problems.
* Solve exponential growth and decay problems.
* Graph exponential functions.
Simple Interest Formula
Simple Interest Formula:
The simple interest I on a principal P at a rate r (expressed as a decimal) per year for t years is
Example 1: (Calculating simple interest)
Juanita has deposited $8000 in a bank for …ve years at a simple interest rate of 6%.
a. How much interest will she receive?
b. How much money will be in her account at the end of …ve years?
Compound Interest
Compound Interest Formula:
A = amount after t years.
P = principal.
r = annual interest rate (expressed as a decimal number).
n = number of times interest is compounded each year.
t = number of years.
Example 2: (Calculating compound interest)
If $100 is deposited in a bank that pays 5% annual interest, …nd the future value A after one year if the interest is compounded
a. annually, and b. quarterly.
Page: 1
Notes by Bibiana Lopez
College Algebra by Kaufmann and Schwitters
5.2
Continuous Compound Interest
Continuous Compound Interest Formula:
A = amount after t years.
P = principal.
r = annual interest rate (expressed as a decimal number).
t = number of years.
e = 2:71828::::
Example 3: (Calculating continuous compound interest)
Find the amount when a principal of $8300 is invested at a 7.5% annual rate of interest compounded continuously for eight
years and three months.
Graphing Exponential Functions
Example 4: (Graphing exponential functions)
Graph the following exponential functions.
a) f (x) = ex
1
2
b) g (x) = e
y
x 3
+4
y
6
8
6
4
4
2
-6
-4
-2
2
2
-2
4
6
x
-8 -6 -4 -2
-2
2
4
6
8
x
-4
-4
-6
-6
-8
Page: 2
Notes by Bibiana Lopez
College Algebra by Kaufmann and Schwitters
5.2
Exponential Decay
Exponential decay occurs when a quantity decreases at a rate proportional to its size. The standard decay formula is:
Example 5: (Exponential decay)
Barium-140 has a half-life of 13 days. If there are 500 milligrams of barium initially, how many milligrams remain after 26
days? After 100 days?
Law of Exponential Growth
Exponential growth occurs when a quantity increases at a rate proportional to its size. The standard exponential growth
formula is:
Example 6: (Exponential growth)
Suppose that in a certain culture, the equation Q (t) = 15000e0:3t expresses the number of bacteria present as a function of
the time t, where t is expressed in hours. Find the initial number of bacteria, and the number of bacteria after 3 hours.
Page: 3
Notes by Bibiana Lopez