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函数：建模关系
如何用函数这一数学思想来表示两个变化中的量之间的关系？
1. Introduction
Introduction
2. Functions
Functions
3. Comparing models and abstract functions
Comparing models and abstract functions
4. Dolbear's law at 92 chirps
Dolbear's law relates temperature to chirp rate by T = 40 + 0.25N. If crickets chirp 92 times per minute, what temperature does the law predict?
5. Valid depth values for the spherical tank model
A spherical tank of diameter 8 meters has volume f(h) = (pi/3)h^2(24 - h) for water depth h. Which choice states the meaningful domain and the reason for it?
6. Volume at nine meters of depth is rejected
For the 8-meter tank, is there a depth h in the model's domain with f(h) = 300 cubic meters? Answer 1 for yes, 0 for no.
7. Volume of the tank at full depth
For the spherical tank f(h) = (pi/3)h^2(24 - h), evaluate f(8) in cubic meters. Round to one decimal place.
8. Model versus abstract function
The rules g(t) = -16t^2 + 32t + 48 and f(x) = -16x^2 + 32x + 48 are algebraically identical. What makes them different functions?
9. Depth after two minutes of draining
A cylindrical tank starts 8 meters deep and drains at a constant 0.5 meters per minute. What is the water depth after 2 minutes, in meters?
10. Domain of the draining models
The drainage models h = q(t) and V = p(t) describe a tank that empties in 16 minutes. What are their domains and the range of the height model?
11. Reading the draining graph in a graphing utility
A graphing utility plots V = p(t) = 256pi/3 - (pi/24)t^2(24 - t) on [0, 16]. What does the plotted curve show?
12. A fixed formula defines one function regardless of context
The formula f(h) = (pi/3)h^2(24 - h) defines the same function with or without the spherical-tank context.