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.

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