Concept explainers
Find the percent of the original amount of dirt is picked up after the seventh time the vacuum is run over the carpet.
Answer to Problem 46PPS
99.99%
Explanation of Solution
Given:
A vacuum claims to pick up 80% of the dirt every time it is run over the carpet. Assuming this is true, what percent of the original amount of dirt is picked up after the seventh time the vacuum is run over the carpet?
Concept Used:
After the first use of the vacuum, pick up 80% or 0.80 from the carpet is cleaned and it will remain 1 − 0.80 = 0.20 still dirty.
After the 2nd use of the vacuum, the still dirty part will be:
Calculation:
Thus a geometric sequence models the problem. We consider
The term
The percent of dirt picked up after the 7th use is:
Thus, 99.99% of the original amount of dirt is picked up after the seventh time the vacuum is run over the carpet.
Chapter 10 Solutions
Glencoe Algebra 2 Student Edition C2014
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