Given:
Function is:
[tex]P(v)=\begin{cases}0.7v+u\text{ if }_0\leq v\leq90 \\ 0.7v\text{ if }v>90\end{cases}[/tex]Find-:
(a)
Value of P(100)
(b)
Average rate of change [ 30, 120]
(c)
Function is linear or not
(d)
P(v)=v
Explanation-:
Value of P(100)
[tex]\begin{gathered} P(100)\text{ is:} \\ \\ v>90 \\ \\ P(v)=0.7v \\ \\ P(100)=0.7\times100 \\ \\ P(100)=70 \end{gathered}[/tex](b)
Average rate of change
[tex]P(v)=\begin{cases}0.7v+u\text{ if}0\leq v\leq90 \\ 0.7v\text{ if}v>90\end{cases}[/tex][tex]P^{\prime}(v)=\begin{cases}0.7 \\ 0.7\end{cases}[/tex]u is constant is then the rate of change is 0.7
(c)
A linear equation is:
Function is:
[tex]y=mx+c[/tex]The given function is a linear function.
(d)
For equilibrium
[tex]\begin{gathered} P(v)=v \\ \\ \end{gathered}[/tex]Check for v
[tex]\begin{gathered} P(v)=v \\ \\ 0.7v+u=v \\ \\ u=0.6v \end{gathered}[/tex]at u = 0.6v function value is equilibrium.