A tank contains 200 liters of fluid in which 30 grams ofsalt is dissolved. Brine containing 1 gram of salt per literis then pumped into the tank at a rate of 4 L/min; thewell-mixed solution is pumped out at the same rate. Findthe number A(t) of grams of salt in the tank at time t.I've attached a photo of the solution to this problem. My question is why it's Rin-Rout instead of Rout - Rin. I don't understand the difference between using Rin-Rout and Rout-Rin. Please provide a clear explanation for this part. we knowdA(t)= Rin - ROLEdtinwhere R = concentration of salt in inflow × input rate = (1gm/ltr)×(4 ltr/min)= 4gm/min=Roi concentration of salt in out flow output rate =A(t)200gm/ltrx (4 ltr/min)=A(t)50gm/mindA(t) A(t)=4-dt50dA(t) 200-A(t)dt50dA(t) 1-dt=200-A(t) 50Above equation is in variable separable form.. on integratingdA(t) = (1/1 dt + C C is constant of integration.200-A(t) 501In(200 A(t)) = ·-t+C5011In=-t+C200-A(t)1200-A(t)1200-A(t)=e50°1200 A(t)= Pe 50*P = ec50by taking exponential power介A(t) 200-Pe 50P is a constant.

See solution in image Explanation:The rate of salt means the rate at which the amount of salt is…

we know dA(t) = Rin - ROLE dt in where R = concentration of salt in inflow × input rate = (1gm/ltr)×(4 ltr/min) = 4gm/min = Roi concentration of salt in out flow output rate = A(t) 200 gm/ltrx (4 ltr/min) = A(t) 50 gm/min dA(t) A(t) =4- dt 50 dA(t) 200-A(t) dt 50 dA(t) 1 -dt = 200-A(t) 50 Above equation is in variable separable form .. on integrating dA(t) = (1/1 dt + C C is constant of integration. 200-A(t) 50 1 In(200 A(t)) = · -t+C 50 1 1 In = -t+C 200-A(t) 1 200-A(t) 1 200-A(t) =e50° 1 200 A(t)= Pe 50* P = ec 50 by taking exponential power 介 A(t) 200-Pe 50 P is a constant.

we know dA(t) = Rin - ROLE dt in where R = concentration of salt in inflow × input rate = (1gm/ltr)×(4 ltr/min) = 4gm/min = Roi concentration of salt in out flow output rate = A(t) 200 gm/ltrx (4 ltr/min) = A(t) 50 gm/min dA(t) A(t) =4- dt 50 dA(t) 200-A(t) dt 50 dA(t) 1 -dt = 200-A(t) 50 Above equation is in variable separable form .. on integrating dA(t) = (1/1 dt + C C is constant of integration. 200-A(t) 50 1 In(200 A(t)) = · -t+C 50 1 1 In = -t+C 200-A(t) 1 200-A(t) 1 200-A(t) =e50° 1 200 A(t)= Pe 50* P = ec 50 by taking exponential power 介 A(t) 200-Pe 50 P is a constant.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter8: Further Techniques And Applications Of Integration

Section8.2: Integration By Parts

Problem 41E

See similar textbooks

Similar questions

Based on data from a research group, a model for the total stopping distance of a moving car in terms of its speed is s=1.9v+0.064v^2, where s is measured in ft and v in mph. The linear term 1.9v models the distance the car travels during the time the driver perceives a need to stop until the brakes are applied. Find ds/dv at v=50 and v=70 mph, and interpret the meaning of the derivative.
The edge of a cube was found to be 30 cm with a possible error in measurement of 0.1 cm. Use differentials to estimate the maximum possible error, relative error, and percentage error in comuting (a) the volume of the cube and (b) the surface area of the cube.
The edges of a cube was measured to be 46 cm with at most possible error of 0.5 cm. Use differentials to estimate the percentage error in the calculated volume. Percentage Error = Note! • Use continuous computations. • DO NOT round off the maximum error and relative error for the calculated volume. • Input numerical values only, do not type the units, space or comma, and percentage sign(3%) • Input your answer in two decimal places ONLY.
Lake Ontario has a volume of approximately V = 1600 km^3. It is heavily polluted by a certain pollutant with a concentration of co =0.1 %. As a part pollution control, the pollutant concentration of the inflow is reduced to cin = 0.02%.The inflow and outflow rates Qin = Qout = Q = 500 km^3 per year. Suppose that pollutant from the inflow is well mixed with the lake water before leaving the lake. How long will it take for the pollutant concentration in the lake to reduce to 0.05%?
Differentiate the function P = 5t³ + 4e*. dP dt
A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a velocity of 42 ft/s. Its height in feet after t seconds is given by y=42t-28t^2. a)Find the average velocity for the time period beginning when t=1 second and lasting for the given time. t=.01 s:t=.005 s:t=.002 s:t=.001 s: NOTE: For the above answers, you may have to enter 6 or 7 significant digits if you are using a calculator. b) Estimate the instanteneous velocity when t=1.
Consider an arterial which has free flow speed of 65 kmph and average running time of vehicles is 145 sec/km determine LOS for this arterial ?
Water is poured into a conical paper cup at the rate of 3/2 in3/sec (similar to Example 4 in Section 3.7). If the cup is 6 inches tall and the top has a radius of 6 inches, how fast is the water level rising when the water is 3 inches deep? The water level is rising at a rate of 2/3pi cm^3/sec
00 L{t}(s) = | te st dt u = dv = -se^(-st) %3D du = 1dt v = e^(-st) 00 00 -t(e^(-st)/s) e^(-st)/-s^2 (e^(-st))/-s^2 -1/s^2 1/s^2
Find the equation of the line normal to x^3 + y^3 = 6xy at (3,3) %3D
f(z)= 5-2z^2 ; z=-2, z=0 a) determine the net change between the given values of the variables. b) determine the average rate of change between the given values of the variable
Find d^2/dt^2(t^10lnt)=