4.2 Logarithmic Functions

If Mary has $1500 in an account at 5.2% compounded continuously, how long will it take for her money to double??

Solving this problem requires the use of logarithms.

Inverse Functions

If x > 0, then the logarithm of x to the base b (b >0, b ≠1),

is the number y such that

That is:

Let’s do a few in base 2 and 3.

Write in Alternate form:

Find:

Inverse Relationship:

Solve:

#22 -2 ln x = 7

#24

Properties of Logarithms

Simplify:

Conversion Formula for logarithms

#38 If , ln x?

#40 If

Graphs of Logarithmic Functions

Domain: Range:

Applications:

#44 COMPOUND INTEREST

How quickly will money double if it is invested at an annual interest rate of 7% compounded continuously?

Doubling Time For the doubling time is

#52 RADIOACTIVE DECAY

The amount of a certain radioactive substance remaining after t years is given by a function of the form . Find the half-life of the substance.

#54 ADVERTISING

The editor at a major publishing house estimates that if x thousand complimentary copies are distributed to instructors, the first-year sales of a new text will be approximately thousand copies. According to this estimate, approximately how many complimentary copies should the editor send out to generate first-year sales of 12,000 copies?

#56 GROSS DOMESTIC PRODUCT

An economist has compiled these data on the GDP of a certain country:

Year	1990	2000
GDP(in billions)	100	180

Use these data to predict the GDP in the year 2010 if the GDP is growing:

a) Linearly

b) Exponentially.