April 2020
Problem of the Month

Coronavirus in Colorado

After viewing graphs of the number of confirmed cases of the coronavirus in China and the U.S. ( Click here to see the graphs), I wondered if the cases in Colorado followed a similar pattern.

Here is the data for the first eighteen days from March 5, 2020 to March 22, 2020 in Colorado:





I gathered the data in the following table so that it can be used in this month's problem:

Day	Cases
0	2
1	8
2	8
3	8
4	12
5	17
6	34
7	49
8	77
9	101
10	131
11	160
12	183
13	216
14	277
15	363
16	475
17	591

Since it appears to be an exponential function, use the data for day #11 (160 cases) and day #15 (363 cases) to solve for A and B in the general exponential function

    y = A e^{B x} .

Now take this equation that you just found and let x = 9, then solve for y to see how close the model is to the actual number of cases.

You must show your algebra to get credit.

Solution to the Problem:

The answers are:

  y = 16.81538 e ^{0.204807 x}

  and

  y = 106.22.


For x = 11:     160 = A e^{11 B}
For x = 15:     363 = A e^{15 B}

Solving for A in the second equation, we get:     A = 363 / (e ^15B)

Now subsitute in the first equation to get:     160 = (363 / (e ^15B))   e ^11B

This simplifies to:     160 = 363   e ^{- 4B}
    or     160   e ^4B = 363

Dividing by 160:     e ^4B = 363 / 160

Now, take the natural log of each side:
    4B = ln (363 / 160)

So, B = 0.204807

Now substitute back to get:
    A = 16.81538

Now take this equation,
  y = 16.81538 e ^{0.204807 x}
  and replace x by 9 to get:

  y = 16.81538 e ^{((0.204807)(9))}
  and therefore y = 106.22.

Correctly solved by:

1. Anna T. Vice	Landon School, Bethesda, Maryland
2. Kelly Stubblefield	Mobile, Alabama
3. James Alarie	Flint, Michigan
4. Brijesh Dave	Mumbai City, Maharashtra, India

Send any comments or questions to: David Pleacher