As part of a modeling problem, I've asked a student to

determine the value of t such that y = 20 * 10^t = 1000.

The answer tells us when to set an expiration date 

so that a bacteria population does not exceed 1000

colony forming units.

​

Since this student does not yet know about logarithms, we're

using the bisection method to automate the trial and error

process.

​

Some possible improvements:

0. Introduce a parameter for max iterations, in case something

   goes wrong.

1. Define y as a function at the top (defined so that 

   algorithm provides a zero of the function).

2. Handle y === 0 separately from y < 0, y > 0.

3. Define a bisect function that performs the algorithm,

   with min, max, and y as parameters, and tolerance as a

   parameter with a default value.

4. Compare algorithm to, e.g.

   https://en.wikipedia.org/wiki/Bisection_method

   https://www.geeksforgeeks.org/program-for-bisection-method/

5. Produce friendlier output using strings.

6. Accept user input through a GUI.

*/

​

let tMin = 1; // minimum value of t in search space

let tMax = 2; // maximum value of t in search space

let midpoint; // midpoint of search space

let population;

let tolerance = 0.1;

​

while (tMax - tMin > tolerance) {

  midpoint = (tMin + tMax) / 2;

  population = 20 * (10 ** midpoint);

  if (population < 1000) { // midpoint is too small

    tMin = midpoint;       // make midpoint the new minimum

  }

  else {                   // midpoint is too big (or it's correct)

    tMax = midpoint;       // make midpoint the new maximum

  }

}

​

console.log(tMin); //lower bound is safest as expiration date

console.log(tMax - tMin); //error does not exceed this value

console.log(20 * (10 ** tMin)); //population at time tMin

console.log(20 * (10 ** tMax)); //population at time tMax