## computergeek123 3 years ago 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?

1. eseidl

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

2. computergeek123

10?

3. eseidl

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

4. eseidl

So, \[l_{0}=5\]\[l_{1}=5*2\]Now we dilate this again,\[l_{2}=(5*2)*2=5*2^2\]seeing a pattern,\[l_{n}=5*2^n\]

5. eseidl

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?

6. computergeek123

What do I do next?

7. eseidl

solve for n

8. computergeek123

like how?

9. eseidl

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

10. eseidl

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

11. computergeek123

Thanks