SOLUTION: Each time a bar of soap is used, its volume decreases by 10%. What is the minimum number of times a new bar would have to be used so that less than one-half its volume remains?

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Question 287588: Each time a bar of soap is used, its volume decreases by 10%. What is the minimum number of times a new bar would have to be used so that less than one-half its volume remains?
(A) 5 (B) 6 (C) 7 (D) 8 (E) 9
Answer by CharlesG2(834) About Me  (Show Source):
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Each time a bar of soap is used, its volume decreases by 10%. What is the minimum number of times a new bar would have to be used so that less than one-half its volume remains?
(A) 5 (B) 6 (C) 7 (D) 8 (E) 9
new
0.9 * new (first use)
0.9 * 0.9 * new (second use) --> 0.81 * new
0.9^3 * new (3rd use) --> 0.729 * new
0.9^4 * new (4th use) --> 0.6561 * new
0.9^5 * new (5th use) --> 0.59049 * new
0.9^6 * new (6th use) --> 0.531441 * new
0.9^7 * new (7th use) --> 0.4782969 * new
C. 7