Population Growth – Exponential and Logistic Models vs. Complex Reality

I. Exponential Population Growth
1a. Suppose a single bacterium is placed in a flask that contains lots of food for bacteria. In this flask, each bacterium grows and divides in two every 30 minutes. Therefore, the number of bacteria in the population doubles every 30 minutes. How many bacteria do you think there willbe by 5 hours after the single bacterium is placed in the flask (just guessing)? ______

1b. Complete the table to calculate how many bacteria there will be at each time.
1 bacterium at the beginning = 0 minutes bacteria by 30 minutes bacteria by 1 hour bacteria by 1 hour and 30 minutes bacteria by 2 hours bacteria by 2 hours and 30 minutes bacteria by 3 hours bacteria by 3 hours and 30 minutes bacteria by 4 hours bacteria by 4 hours and 30 minutes bacteria by 5 hours

2.Plot the number of bacteria at each time; connect the points to show the population growth. Number of Bacteria Time (hours)

3a. How long would it take for the population of bacteria to increase from 1 bacterium to 500 bacteria?

3b. How long would it take for the population to increase from 500 bacteria to 1000 bacteria?

Notice that, when a population doubles in each time interval, the number of bacteria in the population increases faster and faster as the population gets larger. This kind of population growth is called exponential population growth.
4.For these bacteria, population growth can be represented by the mathematical equation:
ΔN = N, where
• N is the number of bacteria at the beginning of a 30-minute time interval
• ΔN (pronounced delta N) is the change in the number of bacteria from the beginning to the end of the 30-minute time interval
Explain the biological reason whyΔN in a 30-minute interval is equal to N at the beginning of the 30-minute