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Base e and Natural Logarithms 10.5. History. The number e is a famous irrational number, and is one of the most important numbers in mathematics. The first few digits are 2.7182818284590452353602874713527 ...

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Presentation Transcript
history
History

The number e is a famous irrational number, and is one of the most important numbers in mathematics. The first few digits are

2.7182818284590452353602874713527...

It is often called Euler's numberafter Leonhard Euler. e is the base of the natural logarithms (invented by John Napier).

slide3

Calculating

The value of (1 + 1/n)n approaches e as n gets bigger and bigger:

vocabulary
Vocabulary

natural base: the number e, which is found using

  • the base rate of growth shared by all continually growing processes
  • Used heavily in science to model quantities that grow & decay continuously

natural base exponential function: an exponential function with base e

vocabulary1
Vocabulary

natural logarithm:a logarithm with base e

The natural log gives you the time needed to reach a certain level of growth.

natural logarithmic function: the inverse of the natural base exponential function

slide6
Ex 1

Ex 2

Use a calculator to estimate to four decimal places.

Ex 3

Ex 4

slide7

Writing Equivalent Expressions

Ex 5

Exponential logarithmic

Write an equivalent equation in the other form.

Ex 6

Ex 7

Ex 8

slide9

Writing Equivalent Expressions

Ex 9

Ex 10

Evaluate

Evaluate

Ex 11

Ex 12

Evaluate

Evaluate

solving equations
Solving Equations

Solve the following equations.

Ex 13

Ex 14

solving equations1
Solving Equations

Solve the following equations.

Ex 15

Ex 16