Possible to create a non-linear gradient?

I've created a vertical gradient (black to white) as a mask layer for an UIImageView, but the linear fade is not working for me.

I want to show more of the full-alpha image and fade quicker towards the bottom, so I was thinking an exponential curve is what I'm looking for. I'd really like to avoid manually adding extra colors/locations, as it will look pretty choppy.

Is there any way to achieve this?

Edit: here's the difference As you can see, there's a lot less black in the exponential one.

I ended up writing my own function, settling on a easeInOutCubic:

let equation: ((Double)->Double) = { x in
    //ease in out cubic
    return x < 0.5 ? 4 * x * x * x : 1 - pow(-2 * x + 2, 3) / 2
}

var colors: [CGColor] = []
var locations: [NSNumber] = []
let min: Double = 0
let max: Double = 1
let steps: Double = 30

for i in stride(from: min, through: max, by: max/steps)
{
    let alpha = 1 - equation(i)
    let location = NSNumber(value: i)

    colors.append(UIColor.black.withAlphaComponent(alpha).cgColor)
    locations.append(location)
}
    
//assign colors/locations to new gradient layer
myGradientLayer = CAGradientLayer()
myGradientLayer.frame = bounds
myGradientLayer.colors = colors
myGradientLayer.locations = locations

//assign gradient layer as mask
layer.mask = myGradientLayer