# Next, your teacher will ask everyone who is infected to raise their hand. How many people were infected?

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2 Estimate how many people you think will be infected after each student has interacted with three other students. After the teacher has come around with the indicator, write down how many people were actually infected. 5. Now you will graph how an infection spreads with increasing numbers of interactions. First, plot a point to indicate that one person was infected before any interactions. How many people would be infected after just one interaction? Add this point to your graph. Next, plot the number of people who were infected after two interactions (from 3 on page 1) and the number of people who were infected after three interactions (from 4 on pages 1-2). Discussion 6. Did the number of people infected increase by the same amount for interaction 1, interaction 2, and interaction 3? Which interaction resulted in the smallest increase in the number of infected people? Which interaction resulted in the largest increase in the number of infected people? In each interaction, each infected person can infect one new person. Therefore an interaction that begins with more infected people will generally result in more new infections. 2

4 To calculate how long it would actually take for the single bacterium to multiply to form a colony of 1000 bacteria, fill in the number of bacteria at each time in the table. 1 bacterium at the beginning bacteria after 30 minutes bacteria after 1 hour bacteria after 1 hour and 30 minutes bacteria after 2 hours bacteria after 2 hours and 30 minutes bacteria after 3 hours bacteria after 3 hours and 30 minutes bacteria after 4 hours bacteria after 4 hours and 30 minutes bacteria after 5 hours How long would it take for the population of bacteria to increase from 1 bacterium to 500 bacteria? How long would it take for the population of bacteria to increase from 500 bacteria to 1000 bacteria? Notice that, when a population doubles every 30 minutes, the number of bacteria in the population increases faster and faster as the population gets larger. This kind of population growth is called exponential growth. To see what exponential growth looks like in a graph, use the data from the above table to plot the number of bacteria at each time in the graph Number of Bacteria Hours 4

5 If exponential growth continued for 10 hours, the original single bacterium would increase to a population of over one million bacteria. This illustrates how exponential growth can result in very rapid increase of population size. In the real world, no population of bacteria or any other biological organism can keep increasing exponentially forever. Why not? All organisms require resources such as water and nutrients to grow and reproduce. The environment where a population is growing has only a limited amount of resources. As the population gets larger, there will not be enough resources to support continued rapid growth of the population. The rate of growth of the population will slow down, and finally the population will reach a maximum size which is called the carrying capacity of the environment. This type of logistic growth curve is illustrated in the following figure. The first part of a logistic growth curve looks like an exponential growth curve, but a logistic growth curve levels off as the population size approaches the of the environment. Logistic Growth Carrying capacity Population Size Time 5

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