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 ≈ 2.718281828459 e is irrational (non-repeating, not-terminating). A function in the form f(x) = Ce bx is a natural base exponential function.
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A famous constant (similar to π) is the natural base, e (also known as Euler’s number).
e ≈ 2.718281828459
e is irrational (non-repeating, not-terminating).
A function in the form f(x) = Cebx is a natural base exponential function.
Let’s take a look at the graph of a natural base exponential function…
.14 .22 .37 .61 1 1.65 2.72 4.48 7.39
Properties of Exponents:
= e6x 4
A = P(1 + r/n)nt
Here is another common investment formula:
A = Pert
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 = Pert
= 5000 • e.085 • 5