Fitting the Model Visually - MA
For this section, you’ll need to have Slide 4: Exponential Model for MA of Modeling Covid Spread (Desmos) open on your computer.
1 Try changing the value of k, then a, then b to find three promising exponential models, graphing each one and labeling your values on the grids below.
a = |
a = |
a = |
Fitting the Model Programmatically - MA
For this section, open your copy of the Covid Spread Starter File.
2 In the space below, define exponential for one of the models you fit in Desmos.
fun exponential(x): ( a * num-expt( b , (~1 * x))) + k end
Two Notes on this function definition:
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num-exptis the function that we use for exponents. It takes in 2 numbers: the base and the power, in this case b and x. -
(~1 * x)at first it may appear that x is being multiplied by negative 1, but it is actually being multiplied by~1(literally the value "roughly 1"). This tells Pyret to round off the calculation, prioritizing speed over precision to get a result that is "roughly accurate". We’ve added this to the function definition so that you won’t have to wait for several minutes for Pyret to runfit-modelto get an answer for question 4.
3 Update the definition for exponential in the Definitions Area and click "Run" to reload it.
Then use fit-model to determine how closely exponential fits the MA-table and fill in the blanks below to interpret the model.
Hint: If you forgot the contract for fit-model, look it up in the contracts pages!
According to this exponential model, on June 9, 2020day zero there were about a + k y-units in MA, for a total of about a + k. This number grew exponentially, increasing 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 about Sunits, which is a(n) bad, ok, good model considering that y-units in this dataset range from lowest y-value to highest y-value.
4 Estimate how many positive cases there will be after X days by looking at graph with your eyes, then use your model to find the answer.
| Using your… | Eyes | Model | Using your… | Eyes | Model | Using your… | Eyes | Model |
|---|---|---|---|---|---|---|---|---|
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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550 days |
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★ Rewrite the model to make Pyret do these calculations with extreme precision. (Remove the part where it multiplies by ~1 .)
WARNING: Be sure to save your work first, as there’s a good chance this will lock up your browser and require force-quitting!
What changed?
Data scientists perform calculations to do things like send satellites to far-away planets, or analyze large populations of a billion or more.
You know that the pros of using ~1 involve speed. What are the potential downsides of using ~1 to speed up a calculation?
These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, 1738598, 2031479, and 1501927). 
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