A tank contains 2 m^3 of water and 20 g of salt. Water containing a salt concentration of 2 g of salt per m^3 of water flows into the tank at a. rate of 2 m^3/min, and the mixture in the tank flows out at the same rate. We call Q(t) the quantity of salt at time t in the tank. In order to have Q(t) lessthanorequalto g, we have to wait for:

A. 6 min

B. 2 ln(6) min

C. 4 In (2) min

D. 2 In(8) min

E. In (8) min

Option E is correct.

t = In 8

Step-by-step explanation:

First of, we take the overall balance for the system,

Let V = volume of solution in the tank at any time = 2 m³ (constant)

Rate of flow into the tank = Fᵢ = 2 m³/min

Rate of flow out of the tank = F = 2 m³/min

Component balance for the concentration.

Let the initial amount of salt in the tank be Q₀ = 20g

The rate of flow of salt coming into the tank be 2 g/m³ × 2 m³/min = 4 g/min

Amount of salt in the tank, at any time = Q

Rate of flow of salt out of the tank = (Q × 2 m³/min)/V = (2Q/V) g/min

But V = 2 m³

Rate of flow of salt out of the tank = Q g/min

The balance,

Rate of Change of the amount of salt in the tank = (rate of flow of salt into the tank) - (rate of flow of salt out of the tank)

(dQ/dt) = 4 - Q

dQ/(Q - 4) = - dt

∫ dQ/(Q - 4) = ∫ - dt

Integrating the left hand side from Q₀ to Q and the right hand side from 0 to t

In [(Q - 4)/(Q₀ - 4)] = - t

In (Q - 4) - In (Q₀ - 4) = - t

In (Q - 4) = In (Q₀ - 4) - t

Q₀ = 20

In (Q - 4) = (In (16)) - t

In (Q - 4) = 2.773 - t

(Q - 4) = e⁽²•⁷⁷³ ⁻ ᵗ⁾

Q(t) = 4 + e⁽²•⁷⁷³ ⁻ ᵗ⁾

For Q to go less than or equal to 6g, we calculate the time it takes to get to 6 g of salt in the tank

In (Q - 4) = (In (16)) - t

t = In 16 - In (Q - 4)

t = In 16 - In (6 - 4)

t = In 16 - In (2)

t = In (16/2)

t = In 8

think about the doctor who treated the major and the speaker in the short story "in another country." put yourself in the shoes of the doctor, and based on what you read in the story, write what you think his thoughts about the major and the speaker would be. use the following vocabulary in your response and change the form of these words as needed: detached resign withered

answer: 12,000

step-by-step explanation: first you ar e supposed to add. then multiply then subtract