This is a greatest integral function, not a piecewise one.
Solution:
Describe the number of tourists is x
The cost of hiring guides is y
So, y = 700 [x/4], x >= 0
{integral function, [x/4] means that the largest integral not exceeding x/4}
The answer is y = 700 [x/4]
The term integral can refer to several different concepts in mathematics. The most common meaning is the fundamental object of calculus corresponding to summing infinitesimal pieces to find the content of a continuous region.
Other uses of "integral" include values that always take on integer values, mathematical objects for which integers form basic examples, and particular values of an equation.
In calculus, an integral is a mathematical object that can be defined as an area or a generalization of an area. Integrals, together with derivatives, are the fundamental objects of calculus. Other words for integral combined antiderivative and primitive. The process of computing an integral is called integration (a more archaic term for integration is quadrature), and the approximate computation of an integral is termed numerical integration.
Another sample about integer values:
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