const int outputPin = 9;
const int pwmIntervals = 100;
float R; // The R value in the graph equation

void setup() {
  pinMode(outputPin, OUTPUT);
  R = (pwmIntervals * log10(2)) / (log10(255));

}

void loop() {
  int brightness = 0;

  for (int interval = 0; interval <= pwmIntervals; interval++) {
    brightness = pow (2, (interval / R)) - 1;
    analogWrite(outputPin, brightness);
    delay(40);
  }
}