Question

The volume of liquid, V litres, in a tank after t seconds, is given by V=5+2/t+1

(a) Calculate the initial volume of liquid in the tank.
(b) Find the rate at which the volume of liquid is decreasing in the tank when t = 3.

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Answer 1

Explanation:

(a)

that means calculate V for t = 0

V = 5 + 2/(0 + 1) = 5 + 2/1 = 7 liters

(b)

for the local slope at a single point we need to create the first derivative.

V' = (5 + 2/(t + 1))' = 2×(1/(t + 1))' = 2×-1/(t + 1)² = -2/(t + 1)²

V'(t = 3) = -2/(3 + 1)² = -2/4² = -2/16 = -1/8

the change rate at t=3 is -1/8.

or

the rate at which the volume is decreasing at t=3 is 1/8.