המנוע המעריכי

function exponentialModel(t, initial, rate) {
  return initial * Math.exp(rate * t);
}

function rateFromSamples(t1, y1, t2, y2) {
  if (y1 <= 0 || y2 <= 0 || t1 === t2) {
    throw new RangeError("positive samples at different times are required");
  }
  return Math.log(y2 / y1) / (t2 - t1);
}

const rate = rateFromSamples(0, 5, 3, 40);
console.log({ rate, doublingTime: Math.log(2) / rate });
console.log(exponentialModel(4.5, 5, rate));

from math import exp, log

def exponential_model(t, initial, rate):
    return initial * exp(rate*t)

def rate_from_samples(t1, y1, t2, y2):
    if y1 <= 0 or y2 <= 0 or t1 == t2:
        raise ValueError("positive samples at different times are required")
    return log(y2/y1) / (t2-t1)

rate = rate_from_samples(0, 5, 3, 40)
print(rate, log(2)/rate)
print(exponential_model(4.5, 5, rate))