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Question

The following table shows the expressions that represent the sales of two companies:

A B

Company
Sales	110(0.70)x	430(1.90)x

Which company has the largest percent of increase? 

A.Company A

B.Company B 

C.Both Company A and Company B

D.Neither Company A nor Company B

Answer 1

Answer B is the correct choice. To determine this answer, one must look at the number in the parentheses in each expression. In the expression for company A, it is 0.70. This actually represents a decrease, as it is a number less than 1 (exactly 1 would be 100%/no change). You may also determine this by setting up the equation: 1 + p = 0.70, where p indicates the percent increase or decrease. When 1 is subtracted from from both sides, the result is p = -0.30, or 30%, with the negative indicating the decrease.

The equation for company B has 1.90 in parentheses; the number is more than one, indicating an increase. The same equation can be applied to prove this: 1 + p = 1.90. Subtract one from both sides and the result is p = 0.90, or 90%, and being positive, represents an increase.

The number outside of the parentheses in each equation represents the starting point of the sales and does not affect the rate of increase.

The x in each equation represents a time factor that can be used to calculate the sales at a certain point of time. However, the problem gives no indication about any time period involved, thus it is irrelevant to the question being asked about percent of increase.

Answer 2

In exponential expressions like the ones in this table, you can identify the coefficient on the front as the initial or principal amount (in this case, 110 and 430 for companies A and B respectively), while the base of the exponent is the part that determines the percent change when x increases in value.

Since multiplication by 1 leaves the original value unchanged, we can think of 1 as the "default multiplier" against which any other multiplier is compared. Thus, for an expression such as "100(1)^x", we can say that there is no percent change involved (neither increase nor decrease). In contrast, if the base of the exponent is smaller than 1, we observe a decrease, and if the base is larger than 1, we observe an increase. The larger the base, the larger the increase (in proportion to the initial amount). Since 1.90 is larger than 0.70, we can say that company B has the larger percent increase of the two.