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11 results for “exponential”

Formulae (11)

A = A_0 e^{kt}

Growth (k>0) or decay (k<0) over time.

e^{i\theta} = \cos\theta + i\sin\theta

Links complex exponentials to trigonometry.

\frac{d}{dx}e^x = e^x

The exponential function is its own derivative.

e^x = \sum_{n=0}^{\infty}\frac{x^n}{n!}

Taylor series of the exponential at 0.

\frac{d}{dx}e^x = e^x

The exponential function is its own derivative.

\int e^x\,dx = e^x + C

Antiderivative of the exponential function.

N_t = N_0 e^{rt}

Unlimited growth of a population over time.

N = N_0\times 2^{t/g}

Exponential bacterial growth by generations.

N = N_0 e^{rt}

Growth of a population at a constant rate.

F_n = 2^{2^n} + 1

Numbers of a special exponential form.

O(2^n)

Runtime that doubles with each added element.