A method which returns a time interval, adjusted for time since initial method call. The caller specifies the initial time (the speed at which an animation might run during first run) and an eventual time (which the time interval will decay towards). Set the kTotalDecayTime to the number of days it will take for the time interval to fully decay.…

DABDecayingAnimationInterval.m

#define kInitialAnimationDate @"InitialAnimationDate"
#define kTotalDecayTime 14 // Number of days for initialTime to decay to eventual time
 
+ (NSTimeInterval)intervalStartingFrom:(NSTimeInterval)initialTime decayingTowards:(NSTimeInterval)eventualTime
{
    NSUserDefaults *defaults    = [NSUserDefaults standardUserDefaults];
    NSDate *creationDate        = [defaults objectForKey:kInitialAnimationDate];
    NSUInteger currentAge;
    
    // Create the date if it hasn't been saved yet
    if ( !creationDate ) {
        [defaults setObject:[NSDate date] forKey:kInitialAnimationDate];
        [defaults synchronize];
        currentAge = 0;
    } else {
        // Set the current age to the number of days since first launch
        currentAge = [creationDate timeIntervalSinceNow] / 60 / 24;
    }
    
    // Determine the % of the decay time which has elapsed
    double days = kTotalDecayTime - currentAge;
    days = days < 0 ? 0 : days;
    
    // Return the adjusted time
    return eventualTime + ( (initialTime - eventualTime) * (days / kTotalDecayTime ) );
}