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(g) Solve the compound interest problem described in Prob. 6.47 (accumulating monthly deposits). Include a provision for either of the following features: (i) (ii) Determine the accumulation (F) resulting from fixed monthly payments (A) for n years. Determine the monthly payment (A) required to accumulate a specified amount (F) after n years.
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(h) Evaluate the polynomial given in Prob. 6.52. Generalize the polynomial so that it can be evaluated using the first n terms, where n is a specified input parameter. (i) Evaluate the area of a triangle, the radius of the largest inscribed circle, and the radius of the smallest circumscribed circle, using the formulas provided in Prob. 6.53(c). Determine the increase in the population of a bacterial culture, using the series expansion given in Prob. 6.53(d). Express the population increase in terms of the ratio P/P0. Enter the values for c, n and t as input parameters.
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8
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Arrays
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8.1 ARRAY CHARACTERISTICS Many applications require the processing of multiple data items that have common characteristics, such as a set of numerical data items represented by x1, x2, . . ., xn. In such situations, it is often convenient to place the data items into an array, where they will all share the same name (e.g., x). The data items that make up an array can be any data type, though they must all be the same data type. (An exception is the variant-type array, where each data item may be of a different data type. However, the use of variant-type arrays is generally considered a poor programming practice.) Each individual array element (i.e., each individual data item) is referred to by specifying the array name followed by one or more subscripts, enclosed in parentheses. Each subscript is expressed as an integer quantity, beginning with 0. Thus, in the n-element array x, the array elements are x(0), x(1), . . . , x(n 1). The number of subscripts determines the dimensionality of the array. For example, x(i) refers to the ith element in a one-dimensional array x. It is helpful to think of a one-dimensional array as a list, as illustrated in Fig. 8.1. (Note that Element 1 corresponds to subscript value 0, Element 2 corresponds to subscript 1, etc.)
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Element n
Fig. 8.1 A one-dimensional array Similarly, y(i, j) refers to an element in the two-dimensional array y. Think of a two-dimensional array as a table, where i refers to the row number and j refers to the column number, as illustrated in Fig. 8.2.
Row 1
Row 2
Row 3
. . . . . . . . .
Row m
Column 1
Column 2
Column 3
Column n
Fig. 8.2 A two-dimensional array
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CHAP. 8]
ARRAYS
Higher-dimensional arrays, such as the three-dimensional array z(i, j, k), are formed by specifying additional subscripts in the same manner. Note, however, that multidimensional arrays can quickly become very large, and hence require vast amounts of storage. You should therefore avoid the temptation to define multidimensional arrays that are unnecessarily large.
8.2 ARRAY DECLARATIONS An array must be declared before it can appear within an executable statement. The Dim statement is used for this purpose. This statement defines the dimensionality (i.e., the number of subscripts), the size (range of each subscript), the data type and the scope of an array (see Chap. 7). Within the Dim statement, each array name must be followed by one or more integer constants, enclosed in parentheses. If several integer constants are present (indicating a multidimensional array), they must be separated by commas. To declare an array within a procedure, the Dim statement is generally written as
Dim array name (subscript 1 upper limit, subscript 2 upper limit, etc.) As data type
Within a module (but outside of a procedure), array declarations are written as
Private array name (subscript 1 upper limit, subscript 2 upper limit, etc.) As data type
Public array name (subscript 1 upper limit, subscript 2 upper limit, etc.) As data type
as discussed in Chap. 7 (see Sec. 7.5). Each subscript normally ranges from 0 to the specified upper limit. Thus, the Dim statement
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