Question

Mar 12: 3

Mar 13: 8
Mar 14: 11
Mar 15: 16
Mar 16: 25
Mar 17: 50

Whats the pattern? Is the pattern linear, quadratic, or exponential? Can you predict the number of cases for march 18, 19 and 20? What about March 25th?

Answer 1

Answer: Mar 18: 125

Mar 19: 318

Mar 20: 743

Mar 25: 15,070

Explanation:

The six seemingly arbitrary points have no common difference or ratio, so cannot be modeled by a linear or exponential function.

The differences of the differences are not constant at any level, so the only polynomial model is 5th-degree. It is ...

(6n^5 -95n^4 +600n^3 -1825n^2 +2814n -1320)/60

where n = days after Mar 11. (Mar 12 corresponds to n=1.) The domain is n ≥ 1.

____

The 5th-degree polynomial increases very fast, but not as fast as an exponential function would.

The values for Mar 12 through Mar 25 are ...

3, 8, 11, 16, 25, 50, 125, 318, 743, 1572, 3047, 5492, 9325, 15070

Explanation:

.

Answer 2

• Mar 18: 125
• Mar 19: 318
• Mar 20: 743
• Mar 25: 15,070

Explanation:

The six seemingly arbitrary points have no common difference or ratio, so cannot be modeled by a linear or exponential function.

The differences of the differences are not constant at any level, so the only polynomial model is 5th-degree. It is ...

(6n^5 -95n^4 +600n^3 -1825n^2 +2814n -1320)/60

where n = days after Mar 11. (Mar 12 corresponds to n=1.) The domain is n ≥ 1.

____

The 5th-degree polynomial increases very fast, but not as fast as an exponential function would.

The values for Mar 12 through Mar 25 are ...

3, 8, 11, 16, 25, 50, 125, 318, 743, 1572, 3047, 5492, 9325, 15070