Question

A water tank contains 75 liters. Water is leaving the tank at an increasing rate given by f(t)=2+0.4t^2 liters per minute.
A) How much water leaves the tank in 10 min?
B) How long will it take for the tank to be empty?
C) What is the average rate of change at which the water left the tank?

Answer 1

Hi there!

A)

We can evaluate an integral to solve:

$\int\limits^{10}_0 {2 + 0.4t^{2}} \, dt = 2(10) + 4/30(1000) = 153.333 L$

B)

Use the FTC to solve:

F(0) - ∫(0 to x min)f(t) = F(x) = 0

$75 - \int\limits^{t}_0 {2 + 0.4t^2} \, dt = 0$

Solve:

$75 = \int\limits^{t}_0 {2 + 0.4t^2} \, dt$

Evaluate:

$75 = 2t + 4/30t^{3}$

Use a graphing utility to solve:

t = 7.65 min

C)

Use the slope formula to find the AROC:

f(10) - f(0) / 10 - 0 = 42 - 2 / 10 - 0 = 4 L/m²