Answer
See details below.
Work Step by Step
The general solution of $y'=4(y-12)$ is
$$y=12+c e^{2t}.$$
When $y(0)=20$, then $20=12+c$, i.e. $c=20-12=8$. In this case
$$y=12+8 e^{4t}.$$
When $y(0)=0$, then $0=12+c$, i.e. $c=-12$. In this case
$$y=12-12 e^{4t}.$$
See the graphs below.
![](https://gradesaver.s3.amazonaws.com/uploads/solution/9220853d-7110-46a1-b905-54f3335fe995/steps_image/small_1575115558.png?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T012428Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=8a4e652487a59f7e1973958329e2accbc5fbde3b4d86cf4bea15b49907f55bd5)