Hey Guys!! A square is cut into 9 smaller squares where each is similar to the original of which 5 are then colored blue. Each of the remaining uncolored squares are cut into 9 smaller squares where 5 out of each group of 9 are colored blue. This process is repeated indefinitely. Write the explicit form of the equation that determines the combined area of uncolored squares after n cuts.
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B) an efficient process

You're asking in the ap section, so i'll give the ap calculus-style answer. alternatively, you can find the vertex of the parabola and use the "y"-coordinate as the answer.

the maximum height can occur at a critical number, that is, a number  such that  .

the derivative of  can be calculated as follows:



find a value of  that is a zero of the derivative:


this is parabola that is opening downward; we can assume there is a maximum at  .

to find that maximum, calculate  .

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Psychologists often talk of the magical number "7" - so it is generally assumed that we can keep 7 (more or less, so 5-9 is the correct answer) items in our short term memory - we know this as a result of many experiments.

we can increase this by chunking, so for example "7 8 9 5 3" is harder to remember than "78 95 3" - try it yourself!

the answer is a)