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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

1) Don't know what to call this; it's sort of but not strictly exponential. If you plot log N vs time, it looks sort of cubic.

2) So maybe N ~ 10^(at³ + bt² + ct + d) is an approximation. I don't possess a TI-84 or similar to try fitting this.

3) From day 40 on, there seems to be a linear increase in log N with time, having average slope of 0.1186 increase in log N per day. Best fit is log N = 0.1186t - 2.91, so N ~ 10^(0.1186t - 2.91). This predicts about 890 MILLION infections by day 100.

4) Likewise, log(10,000,000) = 7 = 0.1186t -2.91, t = 84 days.