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- 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?

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- anonymous

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- anonymous

Well, first off, what will be the length of rectangle B?

- anonymous

10?

- anonymous

Yeah, should be (unless I'm missing something)|dw:1343835098119:dw|

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- 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

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

What do I do next?

- anonymous

solve for n

- anonymous

like how?

- anonymous

First divide both sides by 5. You get:\[2^n=16\]What is n?

- anonymous

Do you understand exponents?
If n=1
\[2^1=2\]If n=2\[2^2=2*2=4\]etc...

- anonymous

Thanks

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