The population of a bacteria sample doubles every hour. If there are 38,400 bacterial cells after 7 hours, how many cells were in the original sample?

*Solution to yesterday’s problem:*

My suggestion for this problem is to break the diagonal into parts that we can handle easily. This is how I divided it:

Now we have two 45-45-90 triangles and one rectangle. We instantly know that the middle segment is 4 cm, because it is the opposite side of the rectangle. As for the 45-45-90 triangles, we can use the Pythagorean theorem to solve for the two legs of the triangle, knowing that both legs are of equal length:

So the left and right segments of the diagonal are both centimeters. Adding those together, we get centimeters. Adding the middle segment, we find that the length of the diagonal is centimeters.

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