Estimating with our Model
1 In the space below, define exponential for the best model from Exponential Models of Covid in Massachusetts.
Answers will vary. If a = 31.6, b = 1.047 and k = 119000, you would get the following:
fun exponential(x): ( a * expt( b , (~1 * x))) + k end
2 Fill in the table below, to show how many positive cases you estimate based on your model after X days.
DO NOT use a calculator, keyboard or mouse! Instead, use only your eyes to look at the formula above or the Desmos graph on your screen.
| After… | ESTIMATED model prediction | How confident are you? (1=Very confident, 5=Not at all) |
|---|---|---|
50 days |
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150 days |
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250 days |
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350 days |
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450 days |
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Fitting Exponential Models in Pyret
3 Define exponential in Covid Spread Starter File. Click "Run" and use fit-model to determine how closely exponential fits the MA-table. Hint: If you forgot the contract for fit-model, look it up in the Contracts Pages!
Answers will vary. Numbers below are provided for reference only!
According to this exponential model, on June 9, 2020day zero there were a total of about (a + k =) a + k y-units in MA. This number increased by a factor of Growth Factor: b or Growth Rate: (b - 1) × 100 % every day.
The error in the model is described by an S-value of ~ Sunits. I agreestrongly agree, agree, disagree, strongly disagree that this model is a good fit considering that y-units in this dataset range from lowest y-value to highest y-value.
4 Use Pyret to compute your model’s predictions after each number of days and fill in the table below.
| After… | ACTUAL model prediction | How close were you? (1=Very close, 5=Very far) |
|---|---|---|
50 days |
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150 days |
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250 days |
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350 days |
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450 days |
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5 If your predictions got worse as the number of days increased, why do you think that is?
These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, 1738598, 2031479, and 1501927). 
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