Question

A storage tank contains 225 gallons of solvent at time t=0. During the interval 0≤ t≤ 10, solvent is being removed from the tank at a rate of L(r)=3+10cos() gallons per hour. During this same interval, clean solvent is being pumped into the tank at a rate of E(t)= 10/2+ln (t²+4) gallons per hour. a. Is the amount of solvent in the tank increasing or decreasing a time t=4 hours? Explain your reasoning.

Answer 1

To determine if the amount of solvent in the tank is increasing or decreasing at t=4 hours, compare the rate of solvent removal with the rate of solvent pumped in.

Step-by-step explanation:

To determine whether the amount of solvent in the tank is increasing or decreasing at t = 4 hours, we need to compare the rate of solvent being removed from the tank to the rate of clean solvent being pumped into the tank.

At t = 4 hours, the rate of solvent being removed from the tank is L(4) = 3 + 10cos(4) gallons per hour. The rate of clean solvent being pumped into the tank is E(4) = 10/(2+ln(4^2+4)) gallons per hour.

If the rate of solvent being removed is greater than the rate of clean solvent being pumped, then the amount of solvent in the tank is decreasing. Otherwise, it is increasing. Evaluate the two rates at t = 4 hours and compare them to determine whether the amount of solvent in the tank is increasing or decreasing.

Answer 2

To determine whether the amount of solvent in the tank is increasing or decreasing at t=4 hours, we need to compare the rate of removal and the rate of pumping at that time.

Step-by-step explanation:

At time t=4 hours, we need to determine whether the amount of solvent in the tank is increasing or decreasing.

The rate at which solvent is being removed from the tank at time t=4 hours can be found by substituting t=4 into the function L(r)=3+10cos(t).

Similarly, the rate at which clean solvent is being pumped into the tank at time t=4 hours can be found by substituting t=4 into the function E(t)=1/2+ln(t^2+4).

If the rate of removal is greater than the rate of pumping, then the amount of solvent in the tank is decreasing. If the rate of removal is less than the rate of pumping, then the amount of solvent in the tank is increasing.

By performing the calculations, we can determine whether the amount of solvent in the tank is increasing or decreasing at time t=4 hours.