Suppose you are a scientist who wants to grow cells. Sample 1 is a cell that divides every twenty minutes. Sample 2 is a cell that divides every thirty minutes. Will there be more cells of Sample 1 or 2 after three hours? How many more?

a. Assuming we are starting out with the same mass or number of both cells, definitely there would be more cells of sample 2 after three hours

b. If there are equal number of both cells initially, there would be 8 times more of cell 2 than cell 1

Step-by-step explanation:

a.The first part of the question asks if there would be more cells of sample 1 or 2 after three hours.

Now, the first assumption we shall be making is that we have equal numbers or let’s say mass of both cells initially.

Okay, let’s say we have x g of both cells initially.

Now sample 1 cell divides every 20 minutes.

How many times will have divided in 3 hours? The correct way to tackle this is by knowing the number of two minutes in 3 hours.

In an hour, we have 3 20 minutes. So in 3 hours, we will have 9 20 minutes

Let’s take a look at the sample 2 cell.

it divides every 30 minutes.

Now, in an hour, we have 2 30 minutes. In 3 hours, we will be having 6 30 minutes

Since cell 2 underwent 6 divisions while cell 1 underwent 9 divisions within the same 3 hours and they both have the same mass initially, then we will have more of cell 2 after three hours.

b. We want to know by how many more.

Now, for cell 1 since the division is 9 times, and it is definitely an exponential division, the mass or amount of the original left after 9 half divisions would be;

(1/2)^9 = 1/512

So 1/512 of x would be left and that would be x/512 left

For cell 2, we have the same approach. There are six divisions.

The amount left after the 6th division would be;

(1/2)^6 = 1/64

So the amount left after the sixth division would be x * 1/64 = x/64

Now, we want to know by which amount is the division of cell 2 greater.

That would be x/64 divided by x/512 = x/64 * 512/x = 8