7.3 The Natural Base e

The Natural Base e A famous constant (similar to π) is the natural base, e (also known as Euler’s number). e ≈ e is irrational (non-repeating, not-terminating). A function in the form f(x) = Ce bx is a natural base exponential function. if b>0…growth if b<0…decay Let’s take a look at the graph of a natural base exponential function…

Ex. Graph f(x) = e x x f(x) –

Ex. Graph f(x) = e x x f(x) –

Simplify. a. e 3 e 5 b. 8e 6 2e 2 c. (2e –3x ) –2 = e 8 = 4e 4 = 2 –2 e 6x = e 6x 4 To simplify natural base expressions, follow the Properties of Exponents:

Recall that we have studied the formula for the value of an investment in which interest is compounded n times per year: A = P(1 + r/n) nt Here is another common investment formula: A = Pe rt A is the balance P is the initial principal r is the interest rate t is the number of years In this formula, the interest is compounded continuously (about every second) Example: For a deposit of $5000 into an account that pays 8.5% interest, find the balance after 5 years if the interest is compounded continuously. A = Pe rt = 5000 e = $

Homework: p #3-39 multiples of 3, #56 and #57