Port of https://bitbucket.org/kluivers/jk-interpolation to Swift.

JKInterpolationMath.swift

//
//  JKInterpolationMath.h
//
//  Created by Carlos Fonseca on 08/11/15.
//  Copyright © 2015 Carlos Fonseca. All rights reserved.
//

import Foundation

func JKLinearInterpolation(t:Float, start:Float, end:Float) -> Float
{
    return t * end + (1.0 - t) * start;
}

//MARK: - Quadratic

func JKQuadraticInInterpolation(t:Float, start:Float, end:Float) -> Float
{
    return JKLinearInterpolation(t*t, start:start, end:end);
}

func JKQuadraticOutInterpolation(t:Float, start:Float, end:Float) -> Float
{
    return JKLinearInterpolation(2*t - t*t, start:start, end:end);
}

func JKQuadraticInOutInterpolation(t:Float, start:Float, end:Float) -> Float
{
    let middle = (start + end) / 2;
    var tt = 2 * t;
    
    if (tt <= 1) {
        return JKLinearInterpolation(tt * tt, start:start, end:middle);
    }
    
    tt -= 1;
    
    return JKLinearInterpolation(2*tt - tt * tt, start:middle, end:end);
}

//MARK: - Cubic

func JKCubicInInterpolation(t:Float, start:Float, end:Float) -> Float
{
    return JKLinearInterpolation(t*t*t, start:start, end:end);
}

func JKCubicOutInterpolation(t:Float, start:Float, end:Float) -> Float {
    let tt = t-1;
    return JKLinearInterpolation(tt*tt*tt + 1, start:start, end:end);
}

func JKCubicInOutInterpolation(t:Float, start:Float, end:Float) -> Float {
    let middle = (start + end) / 2;
    
    var tt = 2 * t;
    
    if (tt <= 1) {
        return JKLinearInterpolation(tt*tt*tt, start:start, end:middle);
    }
    
    tt -= 2;
    
    return JKLinearInterpolation(tt*tt*tt + 1, start:middle, end:end);
}

//MARK: - Exponential

func JKExponentialInInterpolation(t:Float, start:Float, end:Float) -> Float
{
    return JKLinearInterpolation(powf(2, 10 * (t-1)), start:start, end:end);
}

func JKExponentialOutInterpolation(t:Float, start:Float, end:Float) -> Float
{
    return JKLinearInterpolation(-powf(2, -10 * t) + 1, start:start, end:end);
}

func JKExponentialInOutInterpolation(t:Float, start:Float, end:Float) -> Float
{
    let middle = (start + end) / 2.0;
    
    var tt = t * 2.0;
    
    if (tt < 1.0) {
        return JKLinearInterpolation(powf(2, 10 * (tt-1)), start:start, end:middle);
    }
    
    tt--;
    
    return JKLinearInterpolation(-powf(2, -10 * tt) + 1, start:middle, end:end);
}

//MARK: - Sinusoidal

func JKSinusoidalInInterpolation(t:Float, start:Float, end:Float) -> Float
{
    return JKLinearInterpolation(-cosf(t * Float(M_PI_2)) + 1, start:start, end:end);
}

func JKSinusoidalOutInterpolation(t:Float, start:Float, end:Float) -> Float
{
    return JKLinearInterpolation(sinf(t * Float(M_PI_2)), start:start, end:end);
}

func JKSinusoidalInOutInterpolation(t:Float, start:Float, end:Float) -> Float
{
    return JKLinearInterpolation(-0.5 * (cosf(t * Float(M_PI)) - 1), start:start, end:end);
}

Straight port to Swift. I did change one important thing: I'm using Swift's Floats instead of CGFloat, making this pretty straight forward. But you'll probably need to do something like
CGFloat(JKLinearInterpolation(t, start:Float(start), end:Float(end))