ALG-24

Doubling time

Exponential growth.

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Algebradoubling

Governing equation

T_2=\\ln2/k

where

k: k (1/yr)
T_2: T2 (yr)

Lecture brief

Historical brief

From al-Khwārizmī’s restoration to the quadratic formula, AM–GM, De Moivre and logarithms, algebra is the closed-form skeleton under every lab. These sheets solve, bound and compound. This sheet (ALG-24 — Doubling time) is the form associated with doubling. Working symbols: $k$ $\rightarrow$ $T_2$ . Exponential growth.

Purpose

Purpose: compute

T_2

from

k

in Algebra via

T_2=\\ln2/k

Exponential growth. Use it when a real algebra question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

k = 0.070\,\mathrm{1/yr}

, the governing relation

T_2=\\ln2/k

yields

T_2 = 9.90\,\mathrm{yr}

. Exponential growth. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

k k0.07 1/yr

Outputs

T2 T_29.90 yr

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Narration of this film

Exponential growth.

Reading speed

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