The rate of growth of profit (in millions) from an invention is approximated by P'(x) =xe x, where x represents time in years. The total profit in year 1 that the invention is in operation is $20,000. Find the total profit function P(x). Round to the nearest thousandth if necessary.

Q: Five mice in a stable population of 500 are intentionally infected at r= 0 with a contagious disease…

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Q: A sample population of strands of the bacteria is increasing at rate proportional to the population.…

A:

Q: Find the derivative of a power function with the negative exponent y=x−n.

A: We will use the power rule:

Q: Find the derivative of the function f(x) = x√ln x

A: Here given Use the formula of product rule of derivatives as

Q: Initially 35 grams of radioactive substance was present. After 5 hours the mass had decreased by 11…

A: Given:- Initially 35 grams of radioactive substance was present. After 5 hours the mass had…

Q: find nth derivative of y=x/(x+1)^4

A: To find the nth derivative of the function y=x(x+1)4=x+1-1(x+1)4=1(x+1)3-1(x+1)4

Q: Find the derivative of the function. y = x2 ln x

A: We use the product rule to find the derivative

Q: x + x dx x2

A:

Q: use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = ex−12

A: Given function is y=ex-12. To find the derivative of the given function. Solution: Chain rule of…

Q: Find the derivative of the function. y = (ln x)4

A:

Q: Find the first derivative of the function Y = [(x – 1)(2x + 3)]?.

A: Let us see the expansion of (a + b - c)2 formula.(a + b - c)2 = (a + b - c)(a + b - c)(a + b - c)2 =…

Q: A radioactive substance is decaying at a rate represented by y = h(t) = Rqa', in millirems per hour.…

A: Given: The rate of decay of a substance is given by, , where is a initial amount of substance.

Q: For y=ln2x, determine the equation of a tangent line parallel to 2x-3y+1=0

A: here we find the equation of a tangent which is parallel to 2x-3y+1=0. y=mx+c slope = m.

Q: Find the derivative of the function. y = ln√(x2 − 4)

A:

Q: Find an expression for the derivative of the exponential function y=ex using the definition of…

A: To determine the derivative of exponential function y=ex using definition of derivative.

Q: If the instantaneous rate of change of ƒ1x2 with respect to x ispositive when x = 1, is ƒ increasing…

A: As instantaneous rate of change  of f(x) that is f'(x) is positive means the function f(x) is…

Q: Calculate the 4th derivative of the function y=x2/x−1 at x=2.

A:

Q: 8. Create the equation of any function where the instantaneous rate of change when x = 1 does not…

A: Create the equation of any function where the instantaneous rate of change when x = 1 does not…

Q: If the total revenue function for a blender is R(x) = 41x – 0.01x² where x is the number of units…

A: Given that, the revenue R (in dollars) for a blender is given by  R(x) = 41x - 0.01x2 where x is the…

Q: Find the derivative of the function y = ln(9 – e-"). f'(x) =

A: Given that y=ln(9-e-x) To find : Differentiation  y'=f'(x)=ddx(ln(9-e-x))=19-e-xddx(9-e-x)=e-x9-e-x

Q: Find the derivative of the function. h(x) = x² arctan(5x) h'(x) =

A: h(x)=x2tan-1(x)

Q: nown to grow at a rate proportional

A:

Q: Solve for the derivative of y = x(e*) %3D

A: Find your answer below

Q: Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = ex−12

A:

Q: Total net shipments of aluminum (in billions of pounds) are approximated by g(x)=16.2+2.86ln(x+1)…

A: A) Total net shipments of aluminum (in billions of pounds) are approximated by g(x)=16.2+2.86ln(x+1)…

Q: Find the nth order derivative of the square root y=√x.

A: Let's first calculate the nth order derivative of the power function y=xm where m is a real number.

Q: When air expands adiabatically (without gaining or losingheat), its pressure P and volume V are…

A: Pressure and Volume are related by equation At a instant

Q: Find the rate of change of f (x) = x° at x = 2. %3D

A: Rate of change.

Q: Find the derivative of the function  f(x)= e^-3x ln x

A: Given function is

Q: Find the derivative of the function. f(x) = ln(x − 1)

A:

Q: What is the difference of antidifferentiation and anti-derivative?

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Q: Find the derivative of the function. f(x) = ln(x2 + 3)

A:

Q: Find the equation of the tangent line to the graph of f(x) = 4^(x/ln2) at the point where x is ln16.

A: We find dy/dx to find the slope at x.

Q: Find the derivative of the function: f(x)=ln[x^2÷(x+1)^3

A: Formula:

Q: If the total revenue function for a blender is R(x) = 52x − 0.01x2 where x is the number of units…

A: We have the total revenue function R(x) = 52x − 0.01x2.

Q: solve the first and second derivative of Y= (1+lnx)  /  x

A: If y=f(x), then the independent variable x is called the input of the function, and the dependent…

Q: Find the derivative of the function - 3x f(x) = 3 ln(x) + e - df dx

A:

Q: proportional

A: We will solve the problem.

Q: Find the derivative of f(x) = 4e 3x + e -x^2 f(x)= ?

A:

Q: A group of survivors on a supply run has returned to their base camp with a population of 2000. Two…

A: Given:  y       = present number of infected people 2000 = total population  y'(t)  = rate of spread…

Q: Find teh average rate f change of f(x)=3x^(2)-x from x_(1)=-1 to x_(2)=2

A: Solution: The objective is to find the average rate of change of the given function

Q: compute the rate of Change of the functioN at x= a. flx)= -2X²-X,Q= -5 instantaneous

A: Given function: fx=-2x2-x

Q: A radioactive substance is decaying at a rate represented by y = h(t) = Rọa“, in millirems per hour.…

A:

Q: Find the nth derivative of the function y=xlnx at x=1.

A:

Q: Find the nth order derivative of the cube root y=3√x.

A: We first find the first three derivatives using the power rule

Q: Initially 47 grams of radioactive substance was present. After 10 hours the mass had decreased by…

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Q: A bacterial population Y is known to have a rate of growth proportional to Y itself. If between noon…

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Q: Find the 1st derivative of the function: y = 4(Vx + 1)5

A: Given that: y=4(x+1)5

Q: Find the derivative of the function y = ln 5x/(1 − x)

A:

Q: Initially 25 grams of radioactive substance was present. After 10 hours the mass had decreased by…

A:

Exponential Growth Model

The relation that represents an exponential function is: