Question

please help asap i need to hand this in today 13. Competency Check Under ideal conditions, a single bacterium doubles in number every 30 minutes. a) Create a table to show this situation. b) Is this a linear relationship? How do you know? c) Use powers and exponents to create a formula that describes the relationship between time passed and the number of bacteria. d) How many bacteria are there after 5 hours? Assume that none have died.​

Answer 1

Explanation:

a) To create a table that shows the number of bacteria over time, we can start with one bacterium and double it every 30 minutes:

Time (min) Number of bacteria
0 1
30 2
60 4
90 8
120 16
150 32
180 64

b) This relationship is not linear because the rate of growth is not constant over time. The number of bacteria is increasing exponentially, not linearly.

c) We can use powers and exponents to create a formula that describes the relationship between time passed and the number of bacteria. Let's use t to represent the time passed in minutes, and let N(t) be the number of bacteria at time t. We know that the number of bacteria doubles every 30 minutes, so we can write:

N(t) = 2^(t/30)

This formula says that the number of bacteria is equal to 2 raised to the power of the time passed in minutes divided by 30.

d) To find the number of bacteria after 5 hours (300 minutes), we can substitute t = 300 into the formula we just derived:

N(300) = 2^(300/30)

N(300) = 2^10

N(300) = 1024

Therefore, after 5 hours, there are 1024 bacteria, assuming that none have died.