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computergeek123
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?
Well, first off, what will be the length of rectangle B?
Yeah, should be (unless I'm missing something)|dw:1343835098119:dw|
So, \[l_{0}=5\]\[l_{1}=5*2\]Now we dilate this again,\[l_{2}=(5*2)*2=5*2^2\]seeing a pattern,\[l_{n}=5*2^n\]
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?
What do I do next?
First divide both sides by 5. You get:\[2^n=16\]What is n?
Do you understand exponents? If n=1 \[2^1=2\]If n=2\[2^2=2*2=4\]etc...