1) When a quantity (variable n) in an equation is not know and you are trying to evaluate it. For example, if a banana costs 5 cents, how many can you buy for 25 cents. We solve this by saying
Let n be the number of bananas that we can buy for 25 cents, then we have
5 x n = 25 and hence n = (25/5) = 5
2) When you want to express the general term in a series. For example the arithmetic series 1, 4, 7, 10, 13, 16,.......... is really
1, (1+3), (1+6), (1+9), (1+12), (1+15).......... and in general for such an arithmetic series you can find the 100th, 223rd, 567th term without writing down the long chain of numbers. How? we see a pattern in the arithmetic series. If we represent the starting number (1 in our case) as "a"and the equal increment from one term to the next (that's how an aritmetic series is defined) as "r" then the formlua "a + (n-1)r" gives you the n-th number. Remember that in the illustration above 1 is considered the 1st term in the series, (1+3) is the2nd term, (1+6) is the3rd term and so on.
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Assuming you call your number "n", the expression would be "14n". You can replace "n" with whatever variable you want to use.
Roman numerals use letters in place of numbers. An unknown variable in algebra uses a letter instead of a number.
To write the sum of a number and thirty-seven in an algebraic expression, you would use the variable "n" to represent the number. The algebraic expression would be n + 37, where "n" represents the unknown number and 37 represents thirty-seven. This expression represents the sum of the unknown number and thirty-seven.
To write "25 less than a number" as an algebraic expression, you would represent the unknown number as a variable, such as "x." Therefore, the algebraic expression would be written as "x - 25." This expression indicates that you are subtracting 25 from the unknown number represented by "x."
Instead of using W as a variable in your model, you use log(W).