a store is offering a discount of 30% on a suit. There is a sales tax of 6%.
A) using a composition of function, represent this situatio in which the discount is taken before the sales tax is applied.
B) using a composition of functions represent the situation in which the sales tax is applied before the discount is taken.
C) compare the composite functions from parts a and b. does one of them result in a lower final cost? explain why or why not.
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A) To represent the situation where the discount is taken before the sales tax is applied using a composition of functions, we can define two functions: D and T.
Let's assume the original cost of the suit is represented by the function C(x), where x is the original cost. Then the composition of functions representing the situation where the discount is taken first can be represented as follows:
Step 1: Applying the discount:
D(x) = x - 0.3x
= 0.7x
Step 2: Applying the sales tax:
T(x) = (1 + 0.06)D(x)
= 1.06(0.7x)
= 0.742x
Therefore, the composite function representing this situation is C1(x) = 0.742x.
B) To represent the situation where the sales tax is applied before the discount using a composition of functions, we can define two functions: T and D.
Step 1: Applying the sales tax:
T(x) = (1 + 0.06)x
= 1.06x
Step 2: Applying the discount:
D(x) = 0.7T(x)
= 0.7(1.06x)
= 0.742x
Therefore, the composite function representing this situation is C2(x) = 0.742x.
C) Comparing the composite functions from parts A and B, we find that both composite functions yield the same final cost of 0.742x. Hence, both situations result in the same final cost.
However, the order in which the discount and sales tax are applied can affect the individual amounts for discount and tax. If the discount is applied first, the sales tax will be calculated on a lower amount, resulting in a slightly lower final tax amount. On the other hand, if the sales tax is applied first, the discount will be calculated on a higher amount, resulting in a slightly higher discount. But overall, the final cost remains the same in both cases.