(Solved): use this equations(You can derive equations from these equations) and Help me about answer my Contro ...

Main Question Body: Tomato plant can grow by only utilizing the available soil and rain sources. However, with a desired amount of irrigation and fertilization, tomato harvest can be maximized. Question 1: a) Without irrigation and fertilization, a tomato plant reaches maximum $2\mathrm{m}$ where $99.9\%$ of the growth process occurs in 75 days. At $12.5^{\text{th }}$ day, its height is approximately 1.26 $\mathrm{m}$. 1) Derive the model, 2) Obtain the analytic solution, 3) Simulate and analyse it. b) With the fertilization, its height becomes $3.5\mathrm{m}$ in 60 days. 1) Model the tomato plant, 2) Derive its analytical solution, 3) Simulate and analyse. c) With the fertilization and irrigation, it reaches $5\mathrm{m}$ in 60 days. 1) Model the tomato plant, 4) Derive its analytical solution, 5) Simulate and analyse. d) Consider the tomato plant; 1) Classify the system properties, 2) Draw the closed loop block diagram, 3) Reduce the block diagram. it reaches at 12.5 dass to $1.26\mathrm{m}$. it reaches at 75 days to $2\mathrm{m}$. $\begin{array}{l}\frac{\partial x(t)}{\partial t}+2x(t)-bu(t)\Rightarrow dx(t)=bu(t)\\ \frac{x(t)}{u(t)}=\frac{b}{2}\Rightarrow SSG\\ {\lim }_{t\to \infty }x(t)=\frac{b}{2}u(t)=\frac{b}{a}\\ 5x(5)-x(0)+2x(5)=b4(5)\\ x(s)(s+2)=x(0)+bu(s)\\ x(s)=\frac{x(s{)}^0}{s+2}+\frac{b}{s+2}\cdot v(s){\lim }_{t\to \infty }G(s)(t)\\ \begin{array}{ll}x(s)=\frac{b}{s+2}\cdot 4(s)& s+2\cdot (s){\lim }_{s\to \infty }s[5(v(s)\Rightarrow \\ x(s)& 6\end{array}\\ \frac{x(s)}{u(s)}=\frac{b}{s+a}=G(s)\\ G(s)=\frac{b}{s+2}\\ G(t)=\frac{\frac{5+2}{d}}{2}{e}^{-2t}\\ {\lim }_{s\to 0}G(s)u_{sg}\\ {\lim }_{s\to 0}G(0)u_{SG}\end{array}$