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**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 | # of Cases | |||

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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