Modify the "Fading" sketch code below to ramp an LED brightness

exponentially. For the last fifth of the cycle max the brightness

and then repeat the cycle. Use a frequency of $500$mHz $($milli$-$Hertz$).$ A general

plot of one cycle is shown below with normalized time and normalized

brightness.

int ledPin $=9$; $//$ Pin connected to the LED

int brightness $=0$; $//$ Initial brightness level $(0$ to $255)$

int fadeAmount $=5$; $//$ Amount to change the brightness by

void setup$()\{$

$//$ Set the LED pin as an output

pinMode $($ledPin$,$ OUTPUT$)$;

$\}$

void loop $()\{$

$//$ Set the brightness of the LED

analogWrite $($ledPin$,$ brightness$)$;

$//$ Change the brightness for the next loop

brightness $=$ brightness $+$ fadeAmount;

$//$ Reverse the direction of the fade at the ends of the fade

if $($brightness $>=255)\{$

brightness $=0$; $//$ Reset

$\}$

$//$ Wait for $30$ milliseconds before changing the brightness again

delay$(30)$;

$\}$