SOLUTION: Most photocopiers can reduce the size an image by a maximum of 64% of the original dimensions how many reductions at the maximum setting would it take to reduce an image to less th
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Question 798721: Most photocopiers can reduce the size an image by a maximum of 64% of the original dimensions how many reductions at the maximum setting would it take to reduce an image to less than 10% of its original dimensions
I did it logically and I got a answer of 6
But I prefer to do it algebraically using the geometric sequence formula
Show me !!
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
With each reduction, the previous dimensions get multiplied by .
With reductions the original dimensions will be multiplied times ,
and they will end up being multiplied times .
So is our equation
We could say that thew original length would be ,
and the length of the nth reduction would be .
Then we could write that a 10% reduction would reduce to ,
and write -->
From there we can
either start calculating powers of 0.64 until we get to less than 0.1,
or use logarithms.
Calculating powers:
Using logarithms:
--> --> -->
Dividing both sides of the inequality by a negative number, the inequality sign reverses, so
-->
Since we need an integer , we need
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