# Thread: Help with floor function involving bacteria?

1. ## Help with floor function involving bacteria?

I know how to figure this question out if there is a ending amount of hours (such as how many bacteria will be there at the end of 8 hours), but when there is a floor function thrown in there I have no clue how to solve this or where to start. Any help would be appreciated.

The floor function denoted [x], outputs the greatest integer less than or equal to x. So, [7.3]=7, [27]=27, and [-3.5]=-4. A certain strain of bacteria that is growing on your kitchen counter doubles every 5 minutes. Assume that you start with only one bacterium.

a) What quantities are changing in this situation? What quantities are not changing?
b) Use the floor function to define a function that gives the number of bacteria present after t minutes.
c) Represent the number of bacteria present after 30 minutes? How many bacteria are there?
d) How many bacteria are present after 2 minutes? 5 minutes? 14.75 minutes? 23.22 minutes? 47.92 minutes?
e) Determine the approximate number of minutes for the number of bacteria to reach 2000.

2. Hey,

a) so the quantities that are changing should be the time, and the number of bacteria.
b) This is really similar to compound interest or half-life questions.. I'm thinking something like

$B(t) = [(2^{t/5}) x_{0}]$ where B(t) would be the number of bacteria at minute t. and $x_{0}$ is the starting number of bacteria (in our case, 1). So we can see that in 5 minutes, we'll have 2 bacteria, 10 minutes we'll have 4, etc.

The rest of the questions involve using this formula (if it's right... I think it is).

Hope that helps! (Hope you learned from it too!)