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INCLUDEPICTURE "" \* MERGEFORMATINET COVID-19: Exponential Growth and RegressionName ______________________________010618400COVID-19Understanding the SpreadThe SituationIt’s 2020. The World Health Organization has categorized COVID-19 as a pandemic. Our leaders around the world are encouraging us to stay home and practice social distancing. This virus is spreading from infected person to person and as experts work on vaccines, treatment, and understanding how this coronavirus works, we need to do our part to slow it down.Your RoleLet’s sift through the data and see if we can determine the facts about the spread of this pandemic. Look for reputable sources of data online to fill in the italicized prompts and use this information to calculate the follow up questions. We’ll consider some exponential functions to model the spread of this virus and think of some ways to slow the spread.41656014365500 INCLUDEPICTURE "" \* MERGEFORMATINET 461010147465DON’T FORGET020000DON’T FORGET* Exponential Functions have variables as exponents. (ie y=3?7x)* Exponential Growth: f(t)=a1+rt* Exponential Decay: f(t)=a1-rt* r = growth or decay factor* a= initial amount* t= time382905238125Total Coronavirus Cases: Total Recovered: Total Deaths:Use this data to determine the percent of recovered patients:Use this data to determine the percent of death from infection:Why don’t these percentages total to 100%? 00Total Coronavirus Cases: Total Recovered: Total Deaths:Use this data to determine the percent of recovered patients:Use this data to determine the percent of death from infection:Why don’t these percentages total to 100%? WorldwideItaly382905234315Italian Coronavirus Cases: Recovered: Deaths:Use this data to determine the percent of recovered patients:Why do you think this rate is lower than the worldwide rate? 00Italian Coronavirus Cases: Recovered: Deaths:Use this data to determine the percent of recovered patients:Why do you think this rate is lower than the worldwide rate? 382905231775USA Coronavirus Cases: Total Recovered: Population of USA:What percent of the US population is currently infected by coronavirus?00USA Coronavirus Cases: Total Recovered: Population of USA:What percent of the US population is currently infected by coronavirus?USAThe percent of the population infected might seem low, but it’s important to understand that this virus is capable of spreading exponentially. And exponential growth is POWERFUL. Let’s consider a projection of possible virus spread…-149346-162370How quickly a virus spreads from person to person can vary but COVID-19 is particularly easy to spread. Without proper precautions each infected person might infect 2-3 others. Let’s do a few projections based on hypothetical infection rates.1) If only one person is infected to start and each person infects 1 other person every week, this is a 100% growth rate of infected people. (a) Write a formula to represent the number of cases after t number of weeks.Week (t)# of cases012345. (b) Complete the chart to determine the number of cases after each week:(c) Use your formula to find the number of cases after 16 weeks.(d) After how many weeks will it take for the entire population of the USA to be infected?*2) If the rate of infection is such that every infected person, infects another, every 4 weeks (0.25 people/week), respond to the following questions. (a) What is the rate of increase in number of cases per week?(b) Write a formula to represent the number of cases after t number of weeks.(c) Find the number of cases after 16 weeks.(d) After how many weeks will it take for the entire population of the USA to be infected? *It’s important to note that this is a very simplified model. The infection rate fluctuations based on individual’s activity, cleanliness, immune systems, and scope of interactions. Week (since 1/22/20)Cases of infection058017813475,184693,0168198,2383) Exponential Regression: The chart below shows actual worldwide cases of COVID-19 since January 22, 2020. (a) Use exponential regression on your graphing utility to find an exponential equation to model the data. (b) What is the rate of increase of cases of infection per week?(c) If we continue on this projectile, how many people will be infected on week 30 (August 19, 2020)? (e) What percentage of the total population is this?Final Conclusion Now, most importantly, what actions can we take to makes sure that the rate of increase does not remain this high? ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ ................
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