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

Answer:

-24 in^3/sec

Step-by-step explanation:

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

we need to find the rate of change of volume

$\frac{dV}{dt} = \frac{d}{dt} (2000 - 40t + .2t^2)$

Apply power rule to take dervative

$\frac{dV}{dt} = -40+0.4t$

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

Substitute 40 for t

$\frac{dV}{dt} = -40+0.4t$

$\frac{dV}{dt} = -40+0.4(40)$

$\frac{dV}{dt} = -40+16$

$\frac{dV}{dt} =-24$

so its -24 in^3/sec