Question

V(t) = 2000 - 40t + .2t^2. How fast is the volume changing when t=40 seconds?The answer is -24in^3/sec but I need the work that goes with that.

Answer 1

-24 in^3/sec

Explanation:

`V(t) = 2000 - 40t + .2t^2`

we need to find the rate of change of volume

`(dV)/(dt) = (d)/(dt) (2000 - 40t + .2t^2)`

Apply power rule to take dervative

`(dV)/(dt) = -40+0.4t`

we need to find out dv/dt when t=40

Substitute 40 for t

`(dV)/(dt) = -40+0.4t`

`(dV)/(dt) = -40+0.4(40)`

`(dV)/(dt) = -40+16`

`(dV)/(dt) =-24`

so its -24 in^3/sec