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Composite functions are useful when one quantity depends on a second quantity, and in turn that second quantity depends on a third quantity. This is an extremely general situation with lots of real-world applications.
1. The cost of getting new life insurance depends on how old you are, and how old you are depends on what year you were born. Provide an example a composite function using these variables.
2. The amount of time it takes to get to work depends on how much traffic there is, and the amount of traffic there is depends on what time of day it is. If we call the amount of traffic C and the time of day t, then C is a function of t. If we call the time it takes to get to work W, then W is a function of C. Provide an example of a composite function using these variables.
3. Make up your own example of a composite function. Be sure to explain (1) what your variables are, (2) how they are represented in the function, and (3) which elementary functions are combined to form the composite function.
A plane is heading due south with an airspeed of 227 mph. A wind from a direction of 60 degrees blowing at 16 mph. Find the bearing of the plane.
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A cubic polynomial function f is defined by f(x)= 4x^3+ab^2+bx+k where a, b, k, are constants. The function f has a local minimum at x=-2A. Fine the vales of a and b
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If the water level is rising at a rate of 24 cm/min when the height of the water is 3.5 m, find the rate at which water is being pumped into the tank.
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