anonymous
  • anonymous
Agh! Somebody PLEASE help!!!! Joshua is creating a series of rectangles, one inside the other. The length of the first rectangle, Rectangle A, is five inches. Joshua dilates Rectangle A about its center by a scale factor of two to get Rectangle B. He repeats this process using the same scale factor till he gets a rectangle of length 80 inches. How many dilations did Joshua perform including the dilation of Rectangle A?
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
Well, first off, what will be the length of rectangle B?
anonymous
  • anonymous
10?
anonymous
  • anonymous
Yeah, should be (unless I'm missing something)|dw:1343835098119:dw|

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anonymous
  • anonymous
So, \[l_{0}=5\]\[l_{1}=5*2\]Now we dilate this again,\[l_{2}=(5*2)*2=5*2^2\]seeing a pattern,\[l_{n}=5*2^n\]
anonymous
  • anonymous
But, we want to know how many dilations, n, gives us a length of 80. \[5*2^n=80\]Can you take it from here?
anonymous
  • anonymous
What do I do next?
anonymous
  • anonymous
solve for n
anonymous
  • anonymous
like how?
anonymous
  • anonymous
First divide both sides by 5. You get:\[2^n=16\]What is n?
anonymous
  • anonymous
Do you understand exponents? If n=1 \[2^1=2\]If n=2\[2^2=2*2=4\]etc...
anonymous
  • anonymous
Thanks

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