Use Exponential Scale

You can simulate a realistic acceleration of a zoom lens when working with 2D layers by using Exponential Scale, which converts linear scaling of a layer to exponential scaling. This is useful for creating a cosmic zoom, for example. Zooming optically with a lens is not linear—the rate of change of scaling increases as you zoom. To simulate this acceleration, Exponential Scale converts the velocity of the scaling to an exponential curve.

In layer bar mode or in the Graph Editor, hold down the Shift key and select starting and ending keyframes for the scale property.
Choose Animation > Keyframe Assistant > Exponential Scale.

Note: Exponential Scale replaces any existing keyframes between the selected starting and ending keyframes.

AfterEffects

Use Exponential Scale

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