Question

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? A. 16,384 B. 65,536 C. 32,768 D. 9536

Answer 1

C. 32,768

Explanation:

Let's go step by step. (skip to the * sign if you don't wanna follow through everything.)

First, calculate how many sections of 10 minutes there are.

2.5 hours = 2 hours, 30 minutes = 150 minutes.

150/10 = 15

Then, find the equation.

(Truly, you just keep doubling a single bacteria, 1, until you get your desired amount. I'm not sure if there really is a name, sorry!)

Now, we calculate.

1. 1×2=2

2. 2×2=4

3. 4×2=8

4. 8×2=16

5. 16×2=32

6. 32×2=64

7. 64×2=128

8. 128×2=256

9. 256×2=512

10. 512×2=1024

11. 1024×2=2048

12. 2048×2=4096

13. 4096×2=8192

14. 8192×2=16384

15. 16384×2=32768

*

Hence, our answer is Option C.) 32,768.

Hope this helps!

Answer 2

32768

Explanation:

The formula for exponential growth is

y = a b^x where a is the initial value and b is the growth rate and x is the number of times

a = 1

b = 2 since we are doubling

To find x we take the amount of time we have 2.5 hours = 2.5 *60 = 150 minutes divided by the 10 minute doubling time

150/10 = 15 times

y = 1 * 2^ 15

y =32768