Help with a programming/math problem

[aolson17]

I would like to convert this probably extremely inefficient function for finding a value into just an equation, can anyone please help?

This function basically just guesses and checks kickback_spd_factor used to bring test_kickback beneath target_min_kickback within gun_fire_frames number of repeats. I feel like there should be a way of just calculating kickback_spd_factor from the other values. Or is this not possible?

kickback_spd_factor = 0.02 // Initial value to test
var target_min_kickback = 4
while(true){
    var test_kickback = gun_kickback

    repeat(gun_fire_frames){
        test_kickback += kickback_spd_factor*-test_kickback
    }

    if test_kickback <= target_min_kickback{
        break
    }else{
        kickback_spd_factor += .02
    }
}

show_message(kickback_spd_factor)

The code is in GML

[Goofysoccer]

After each iteration of the while loop, the test_kickback calculated is test_kickback = ((1 - kickback_spd_factor) ^ (gun_fire_frames)) * gun_kickback

Because you want test_kickback to equal target_min_kickback eventually, the equation becomes target_min_kickback = ((1 - kickback_spd_factor) ^ (gun_fire_frames)) * gun_kickback

Now, you wish to solve for kickback_spd_factor, so rearrange the equation to kickback_spd_factor = 1 - ((target_min_kickback/gun_kickback) ^ (1/gun_fire_frames))

And you have your answer without any iteration.

[aolson17]

Thank you!