Question

A certain bacterial culture is multiplying in a culture dish, doubling in size every 10 minutes. It takes exactly two hours to fill the whole dish. How long does it take to fill half the dish?

Answer 1

Ok so the equation would be
amount = number of bacteria originaly *optional* × 2^(number of minutes divided by 10)
It's the number of minutes divided by 10 because it doubles every 10 minutes.
So if it took two hours for all of it to fill, it would've been 120 minutes so 12 10 minutes.
2^12
So half of that would be 60
I think it takes an hour if you divide it --- the rest is just extra calculation

Answer 2

110 Minutes

Explanation:

First, let's find out how much bacteria were in the bowl at the end of two hours. We will use a modified Geometric Sequence Explicit Formula for this.

`a_(n)` =
`a_(i\\\\)` ×
`r^(n\\)`

Where n is the generation of bacteria you are trying to find, i is the initial amount of bacteria, and r is the ratio of bacteria.

The generation is equal to 12. This is because the time interval is 10 minutes, which fits 12 times into two hours (120 minutes).

The variable i is equal to 1 since the bacteria dish began with one bacterium.

The ratio (r) is equal to 2 since bacteria split in half to reproduce, therefore doubling in number.

That gives us the equation: 1 ×
`2^(12\\)`, which equals 4096.

Now, we have to find out how long it took for the bacteria to be half of that. Because we know that bacteria double in size every 10 minutes, we know that the bacteria dish is two times as big as it was 10 minutes ago, in other words, 10 minutes ago it was half it's size. That means that it took 120 - 10 minutes, or 110 minutes, for the bacteria dish to be full.

We can check this with the equation: 1 ×
`2^(11)`. This is equal to 2048. This is half of 4096, so we know the answer is correct.