A tank contains 50 lb of salt dissolved in 500 gallons of water. A brine solution is pumped into the tank at a rate of 5 gal/min; it mixes with the solution there, and then the mixture is pumped out at a rate of 5 gal/min. Determine A(t), the amount of salt in the tank at time t, if the concentration of salt in the inflow is variable and given by Cin(t) = 2 + sin(t/4) Ib/gal. A(t) = Ib

Q: t du/dt = u - u2 ln(t)

A:

Q: Suppose that a motorboat is moving at 49 ft/s when its motor suddenly quits, and that 9 s later the…

A: Sol:- We can solve this problem by using the differential equation dv/dt = -kv, where v is the…

Q: The instantaneous rate of change of a ball (in ft/s) is given by f'(x) = √x Select one: 1 4 O a. sec…

A:

Q: During the time interval 0 < t< 11, the rate at which the depth of snow on the ground is changing,…

A:

Q: An object is suspended from the end of a spring. Its displacement, in cm, from the starting position…

A: We will find out the required values.

Q: A respiratory cycle is defined as the beginning of one breath to the beginning of the next breath.…

A:

Q: By using the exponential definitions of sinh and cosh. show that cosh (t) - sinh (t)

A:

Q: *- y = ey %3D

A:

Q: Use implicit differentiation to find dv/dL.

A: We will use concepts of differentiation in this.

Q: = sin(5x) for y(0) = 2

A: the solution is, y = (11 - cos5x)/5  The detailed solution is as follows below:

Q: "ind f'(x), where f(x) is the inverse function of y = cos T, x E [T?, 472].

A:

Q: A typical human heart pumps 70 milliliters(mL) of blood with each heartbeat. Assuming a heart rate…

A: The Fundamental Theorem of Calculus (FTC) states that ∫abf'(x)dx=Fb-F(a), where F(x) is the…

Q: Find the given derivative 6 Dx 7x 1 Dx 7x 5 LN +

A:

Q: A square-shaped sheet of ice is growing as time passes. If the sheet of ice is always in the shape…

A:

Q: e velocity of a particle is given as h(t) = sin(t) m/s where t is measured in nds, what is the…

A:

Q: Let f(x) = cos(3/7). Find f'(x). f'(z) =

A: Recall: df(g(x))dx=f'(g(x)).g'(x) dcos xdx=-sinx dxndx=nxn-1

Q: a)    Determine the rate of change for the following functions (i) to (iii):   B=10 B is the value…

A:

Q: Find f'(x) and f'(c). Function Value of c x² -9 f(x) = C = 1 X - 9 子(x) f'(c) %3D

A: Hi there, at a time we can answer only one question and the exact one was not specified. So, I have…

Exponential Growth Model

The relation that represents an exponential function is: