Question

I’m not really sure I’m how to approach and solve this problem please help

Answer 1

Given:

Function is:

`P(v)=\begin{cases}0.7v+u\text{ if }_0\leq v\leq90 \\ 0.7v\text{ if }v>90\end{cases}`

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)

`\begin{gathered} P(100)\text{ is:} \\ \\ v>90 \\ \\ P(v)=0.7v \\ \\ P(100)=0.7*100 \\ \\ P(100)=70 \end{gathered}`

(b)

Average rate of change

`P(v)=\begin{cases}0.7v+u\text{ if}0\leq v\leq90 \\ 0.7v\text{ if}v>90\end{cases}`
`P^(\prime)(v)=\begin{cases}0.7 \\ 0.7\end{cases}`

u is constant is then the rate of change is 0.7

(c)

A linear equation is:

Function is:

`y=mx+c`

The given function is a linear function.

(d)

For equilibrium

`\begin{gathered} P(v)=v \\ \\ \end{gathered}`

Check for v

`\begin{gathered} P(v)=v \\ \\ 0.7v+u=v \\ \\ u=0.6v \end{gathered}`

at u = 0.6v function value is equilibrium.