Calculus › Section F · Logarithmic, exponential, and other transcendental functions › Topic F.5
Other bases and compound growth
Not every exponential is written in base e: computing loves base 2, chemistry loves base 10. All of them turn out to be e in disguise, and one conversion factor runs the whole family.
In this topic
- What is 2^x, really?
- One logarithm family, rescaled
- The derivative of a^x
- d/dx of the general logarithm
- Worked example: the slope of 2^x where it crosses the y-axis
- Worked example: integrating any base
- Compound interest, from annual to continuous
- Doubling and decay language
- Common mistakes to avoid
- Key takeaways
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Standards: 2