# A particular strain of bacteria doubles in population every 10 minutes. Assuming you start with a single bacterium in a petri dish, how many bacteria will there be in 2.5 hours?

##### 1 Answer

#### Explanation:

The trick here is to realize that you can express the *increase in population* as a **power of**

You know that every **minutes**, the number of bacteria will **double**. If you take *initial number of bacteria*, you can say that

#x_0 * 2 -># after#10# minutes

#(x_0 * 2) * 2 = x_0 * 2^color(red)(2) -># after#color(red)(2) * 10# mintues

#(x_0 * 2^2) * 2 = x_0 * 2^color(red)(3) -># after#color(red)(3) * 10# minutes

#(x_0 * 2^3) * 2= x_0 * 2^color(red)(4) -># after#color(red)(4) * 10# minutes

#vdots#

and so on. As you can see, you can say that the number of bacteria present after **minutes**,

#color(purple)(|bar(ul(color(white)(a/a)color(black)(x = x_0 * 2^n)color(white)(a/a)|)))#

Here

**number of** **minute** intervals that pass in

In your case, you know that

#2.5 color(red)(cancel(color(black)("h"))) * "60 min"/(1color(red)(cancel(color(black)("h")))) = "150 minutes"#

So, how many

#n = (150 color(red)(cancel(color(black)("min"))))/(10color(red)(cancel(color(black)("min")))) = 15#

Since you start with a single bacterium in a Petri dish, you have

#color(green)(|bar(ul(color(white)(a/a)color(black)(x = "1 bacterium" * 2^15 = "32,768 bacteria")color(white)(a/a)|)))#