Growth over time with variable growth rate?

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X increases Y + Z times per time unit:

X = X + (time * (Y + Z) )

The value of Z is constant Z = 1, value of Y starts at Y = 2.0 and is decaying at speed of 0.5 per time unit.

Is it possible to use equation to predicate the value of X after N time units, witch the assumption that Y (growth rate) could have reached zero somewhere in mid of time-frame?

Example: time T = 6

0 - growth = 1 + 2.0
1 - growth = 1 + 1.5
2 - growth = 1 + 1.0
3 - growth = 1 + 0.5
4 - growth = 1
5 - growth = 1
6 - growth = 1

Is it possible to show it with math equation?