The rate of change is how much a quantity have changed relative to another,
Let:
[tex]P \to[/tex] Pressure
[tex]V \to[/tex] Volume
Where:
[tex]V(p) = \frac 1p[/tex]
(a) Average rate of change from p = 7 to 8.
The average rate of change (m) is calculated using:
[tex]m =\frac{V(p_2) - V(p_1)}{p_2 - p_1}[/tex]
So, we have:
[tex]m =\frac{V(8) - V(7)}{8-7}[/tex]
[tex]m =\frac{V(8) - V(7)}{1}[/tex]
[tex]m =V(8) - V(7)[/tex]
Calculate V(8) and V(7)
[tex]m = \frac 18 - \frac 17[/tex]
Take LCM
[tex]m = \frac {7-8}{42}[/tex]
[tex]m = -\frac {1}{42}[/tex]
(b) The Rate of change at p = 7
We have:
[tex]V(p) = \frac 1p[/tex]
Differentiate, to calculate the rate of change of V with respect to P
[tex]V' = -\frac 1{p^2}[/tex]
Substitute 7 for p
[tex]V' = -\frac 1{7^2}[/tex]
[tex]V' = -\frac 1{49}[/tex]
Hence, the rate of change with respect to p at p = 7 is -1/49
Read more about rates of change at:
https://brainly.com/question/13103052
