Скачать или смотреть Calculus 1, Lesson 1.2: Exponential Functions

Exponential functions P=f(t)=P0*a^t are very important kinds of functions. They model situations where the relative percent rate of change of P with respect to t is a constant. They have applications to compound interest and depreciation. Doubling time and half life are important properties of exponential functions. Infinite Powers, How Calculus Reveals the Secrets of the Universe: https://amzn.to/37PBMjb.

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⏱️TIMESTAMPS⏱️
(0:00) Calculus is the science of continuous change and functions model change
(0:34) Review linear functions from Lesson 1.1
(2:32) Graphical comparisons of linear versus exponential growth
(3:03) Doubling growth (100% relative growth per unit time)
(4:09) Tripling growth (200% relative growth per unit time)
(5:26) Compound interest effective interest rates based on nominal interest rates
(8:43) Continuity and growth questions
(9:20) General exponential growth and decay functions
(11:22) Graphs of exponential growth and decay functions
(12:09) Car depreciation example
(13:28) Compounding more and more often (for compound interest)
(14:55) The number e (as a limit of compound interest)
(15:48) Continuous compounding (for compound interest)
(17:07) Exponential functions base e
(18:46) Doubling time and half life
(19:59) Exponential functions are continuous
(21:02) Interest is actually paid at discrete times, so the actual model is discontinuous

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