# Problem of the Day: 2/9/13

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:

$s^2+s^2=(4)^2$

$2s^2=16$

$s^2=8$

$s=\sqrt{8}=2\sqrt{2}$

So the left and right segments of the diagonal are both $2\sqrt{2}$ centimeters. Adding those together, we get $4\sqrt{2}$ centimeters. Adding the middle segment, we find that the length of the diagonal is $4+4\sqrt{2}$ centimeters.