I need help with this homework plz

Question

Data for coronavirus for US is shown.

number of days Total number of infection

0 1

10 6

20 12

30 15

40 69

50 1025

58 9415

100 ?

? 10,000,000

1)What type of model is this?

2)Enter the function that the model fits

3) if the rate continues how many total infections in 100 days?

4)if no modifications were made to change this pattern, after how many days would there have been 10,000,000 infections?

Answer 1

This is definitely an exponential function. Here is the scatter plot:

See how it skyrockets so quickly.

If you plug the data points into a TI-84 calculator, it will give you the following equation as the Least Squares Regression model using ExpReg (exponential regression):

y = 0.7009295312(1.153978133)^x where x in the number of days and y is the total number of infection.

However, this model does not do well in predicting the number of infected at 58 days (it predicts 2,839 while the data shows 9, 415). So it makes me question how well it will predict the number of infections at 100 days and also the number of days when the number of infections are 10 million. But, I'll use the model and predict the number of cases at 100 days. It says there would be 1,162,605 infection and shows that on day 115.02579, there are 10 million infections.

When we try Desmos, we get a different exponential regression function (I'm not sure why the models are different). It gives the function as:

y = 0.000986191(1.3193)^x

This model does poorly at low numbers of days (at 30 days, it predicts 4 when the data shows 15) however, at 50 days, it shows 1026 (almost exactly on) and at 58 days, it shows 9416 (again almost exactly on). This makes me feel like this model might give better estimates for the prediction of the number of infections at 100 days and the number of days when the number of infections are 10 million. At 100 days, it predicts 1,067,375,620 infections (that's over a billion) and is probably not realistic. It shows that there are 10 million infections on day 83.14561.

The best answer, knowing that there are only a limited number of people, would probably be to use a logistics curve. But that might be a little above the level of Algebra 2.