Anonymous

### Question Description

Modeling Growth of Coronavirus Cases

The two graphs below show the growth in confirmed cases and in deaths due to coronavirus in China in January, 2020.

If we draw a smooth curve for the number of confirmed cases, then find points on this graph, we would get the following table.

1. Translate the table so the first point has an x-value of 0. Show the translation used.

 Day in January x # of Cases y 13 1 0 1 14 2 15 3 16 5 17 10 18 17 19 30

2. If we use larger values for y, we will get a better estimate of the common ratio b by dividing consecutive y-values. Estimate the value of b by dividing 30 by 17. Round of the answer to the nearest 100th.

3. The value of a in our model can be found in the translated table by finding the value of y when . We call this the initial value, in this case, the initial number of confirmed cases. Find the value of the parameter a.

4. An equation representation of the table of values will fit the form . Write the equation model by replacing a by the value found in question 3, b by the value found in question 2, and by the translation used in question 1.

5. To see if the model is reasonable, replace x in your equation model by 19. Do you get a number close to 30?

6. If you replace x in your equation model by 27, you should get a y close to 2,744. Do you?

7. Use your equation model to predict the number of cases on January 31, 2020.

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