If the growth rate is constant, you could calculate the growth rate (e.g. pixels per second) and use that to extrapolate to the final size.
E.g. if the logo appears at time 0:40, begins fading out at 0:48, and becomes entirely invisible at 0:50, you could measure the size at time 0:40 and 0:48.
If you get the width at those times to 150 pixel and 310 pixel, you now know that it has grown by 160 pixel within 8 seconds, or 20 pixels per second. Since it continues growing for another 2 seconds, the final size at time 0:50 when it has become invisible must be 160 (pixels) + 2 (seconds remaining) * 20 (pixels/second) = 200 pixels.
Of course, since video frame times rarely fall on nice, round numbers, you have to calculate the times and time differences with decimals, meaning you will most likely also end up with non-whole pixel sizes. You'll just have to round off the final size you calculate, but keep using full precision until then.
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