4. Air purification devices in the room clean the air. The airflow over time for the first device changes according to the formula $f(t)=2^{t}$, and for the second device, it is $f(t)=2^{t+3}$. In the room, there are four devices of the first type and one of the second type. $S$ how many purification devices with a flow rate of $f(t)=2^{t+2}$ could replace the existing ones?
4. We set up the equation $4 \cdot 2^{t} + 2^{t+3} = a \cdot 2^{t+2}$. We simplify the equation by factoring out the common factor $2^{t}(4 + 8 - 4a) = 0$. We observe that $2^{t} \neq 0$. Therefore, $4 + 8 - 4a = 0$. Solving for $a$, we get $a = 3$.

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