Intermediate Algebra (11th edition)

CAUTION Do not reject a potential solution just because it is nonpositive.

Reject any value that leads to the logarithm of a nonpositive number.

616 CHAPTER 10 Inverse, Exponential, and Logarithmic Functions

Solving a Logarithmic Equation Step 1 Transform the equation so that a single logarithm appears on one side.Use the product rule or quotient rule of logarithms to do this.

Step 2 (a)Use Property 4.If then (See Example 4.) (b) Write the equation in exponential form.If then x=bk.(See Examples 3 and 5.)

logb x= k,

logb x= logb y, x= y.

OBJECTIVE 3 Solve applications of compound interest. We have solved

simple interest problems using the formula

Simple interest formula

In most cases, interest paid or charged is compound interest(interest paid on both

principal and interest). The formula for compound interest is an application of expo-

nential functions. In this book, monetary amounts are given to the nearest cent.

I=prt.

Compound Interest Formula (for a Finite Number of Periods)

If a principal of Pdollars is deposited at an annual rate of interest rcompounded

(paid) ntimes per year, then the account will contain

dollars after tyears. (In this formula, ris expressed as a decimal.)

APa 1

r

n

b

nt

Solving a Compound Interest Problem for A

How much money will there be in an account at the end of 5 yr if $1000 is deposited

at 3% compounded quarterly? (Assume no withdrawals are made.)

Because interest is compounded quarterly, The other given values are

(because ), and

Compound interest formula

Substitute the given values.

Simplify.

Use a calculator. Round to the nearest cent.

The account will contain $1161.18. (The actual amount of interest earned is

$1161.18- $1000= $161.18.Why?)

A= 1161.18

A= 10001 1.0075 220

A= 1000 a 1 +

0.03

4

b

4 # 5

A= Pa 1 +

r

n

b