Prediction of the ratio

Suppose there is a jar with 100 marbles of which 80 are red and 20 are blue (80/20 ratio or pred = 0.8). Each day 20 randomly chosen marbles out of those original 100 are replaced by 20 new marbles of which only 9 are red and 11 are blue (45/55 ratio or pred new = 0.45). So, for example 20 marbles are taken out of the jar. 16 are red, 4 blue. They get replaced with 9 red and 11 blue marbles. Now 73 marbles in the jar are red and 27 are blue.

I want to plot it as a sequence of expected values like so:

Day Expected number of red marbles
0 80
1 73
2 67
3 64
... ...
n 45

How to calculate the expected value for each day using a formula?

Each day you remove $$\frac15$$ of the marbles, so on average you expect to remove $$\frac15$$ of the red marbles. Then you add another $$9$$ red marbles. So if $$e_n$$ is the expected number of red marbles on day $$n$$, then $$e_{n+1}=\frac45e_n+9\ ,\qquad e_0=80\ .$$ This can be solved by standard methods to give $$e_n=35\Bigl(\frac45\Bigr)^n+45\ .$$