2 HistoryThe number e is a famous irrational number, and is one of the most important numbers in mathematics. The first few digits areIt is often called Euler's number after Leonhard Euler. e is the base of the natural logarithms (invented by John Napier).
3 The value of (1 + 1/n)n approaches e as n gets bigger and bigger: n CalculatingThe value of (1 + 1/n)n approaches e as n gets bigger and bigger:n(1 + 1/n)n125101001,00010,000100,000
4 Vocabulary natural base: the number e, which is found using the base rate of growth shared by all continually growing processesUsed heavily in science to model quantities that grow & decay continuouslynatural base exponential function: an exponential function with base e
5 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
6 Use a calculator to estimate to four decimal places. Ex 1Ex 2Ex 3Ex 4
7 Writing Equivalent Expressions Exponential logarithmicWrite an equivalent equation in the other form.Ex 6Ex 5Ex 7Ex 8