Story: COVID-19 has broken out!! As a member of the Center for Disease Control and Prevention (CDC), your team has been tasked with analyzing data to predict the behavior of the disease and creating a report based on your findings.

1. This data represents the number of COVID-19 cases worldwide from January 20, 2020 (t=1) to February 5, 2020 (t=15). Graph the following data on the graph paper.

The number of COVID-19 cases worldwide from January 20, 2020 to February 5, 2020

2. Given your graph, draw a best fit exponential curve.
3. Using your best fit curve, find the exponential function that models the data (Model 1).
4. Find the growth rate for the model.
5. Given your exponential model, predict what will happen one month after the initial spread of the disease. What about 1 year? Do you agree with these numbers? Why or why not

Model 1: Total cases (exponential function)

exponential function model for number of cases

Equation of line of best fit: $LaTeX: y=647.42e^{0.2755x}$
Growth rate: $LaTeX: y'=647.427\left(0.2755\right)e^{0.2755x}$
Relative Growth rate: 27.55 % per day
Doubling Time: 2.5 days

Using the exponential model, the number of people infected one month after the initial spread of the virus would be about $LaTeX: 3.3\times10^6$ . One year after the initial spread, the infected population would be approximately $LaTeX: 3.0\times10^{46}$ . This exponential rate of growth obviously cannot be sustained, because the total human population on Earth is approximately $LaTeX: 8\times10^9$ . Therefore, at some point the curve must begin to flatten rather than continue to grow exponentially.