Standard printer paper has a thickness of 0.1mm. write an equation for a function that should approximately the thickness of a s
1 answer:
Folding a paper will make it thickness become double from it before.
Unfolded paper has 1 thickness
1 times folded paper has 2 thickness
2 times folded paper has 4 thickness
3 times folded paper has 8 thickness
From here it is clear that the pattern is
. SInce the paper is 0.1mm, then the function would be:
f(n)= x 0.1mm
Unfolded paper has 1 thickness
1 times folded paper has 2 thickness
2 times folded paper has 4 thickness
3 times folded paper has 8 thickness
From here it is clear that the pattern is
f(n)=
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The question is an illustration of equivalent ratios.
- 3 cups of dark orange require 3 ounces of yellow paint
- 3 cups of light orange require 19.5 ounces of yellow paint
1 cup of dark orange requires
To make 3 cups, we simply multiply by 3, because
So, we have:
2 cups of light orange require
To make 3 cups, we simply multiply by 1.5, because
So, we have:
Hence:
- 3 cups of dark orange require 3 ounces of yellow paint
- 3 cups of light orange require 19.5 ounces of yellow paint
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Take the logarithm of both sides. The base of the logarithm doesn't matter.
Drop the exponents:
Expand the right side:
Move the terms containing <em>x</em> to the left side and factor out <em>x</em> :
Solve for <em>x</em> by dividing boths ides by 5 log(4) - log(3) :
You can stop there, or continue simplifying the solution by using properties of logarithms:
You can condense the solution further using the change-of-base identity,