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特殊的数
为什么形如 $f(t) = b^t$（其中 $b \gt 0$ 且 $b \ne 1$）的每个指数函数都可以看作某个特殊指数函数的水平伸缩？
1. Introduction
Introduction
2. The natural base
The natural base
3. Why any exponential function can be written in terms of
Why any exponential function can be written in terms of
4. Summary
Summary
5. Aligning two exponential bases
For what k does 2^(kt) equal 3^t for all t?
6. Limit of the average rate near one
The average rate of change of e^t on the small interval [1, 1+h] approaches a special number as h shrinks toward zero. What is that number, to four decimal places?
7. Solving e-to-the-t equals two
Solve e^t = 2. What is t, to four decimal places?
8. Solving a shifted exponential equation
Solve 2e^t - 4 = 7. What is t, to four decimal places?
9. Solving a decaying exponential equation
Solve 4 - 2e^(-0.7t) = 3. What is t, to four decimal places?
10. Comparing compounding frequencies
With P = 100, r = 0.08 and one year, how does the balance change as compounding goes from quarterly to monthly to weekly?
11. Base-k exponential family
For g(t) = e^(kt), how does k control the graph, and what is the long-run behavior of F(t) = 74.4 - 38.8 e^(-0.05t)?
12. Every exponential can be rewritten with base e
For any positive base b, the function b^t equals e^(kt) for some constant k.