The percent of research articles in one prominent journal written by researches in the Unites States during 1983-2003 can be modeled by  A ( t ) = 30 + 28 1 + .08 ( 1.02 ) − t where t is time in years since 1983. Numerically and/or graphically estimate l i m x → ∞ A ( t ). (Do not include units or symbols.)

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A:

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A: Mirror image with reference to y-axis: Given a function f(x), a new function g(x)=f(−x) is a…

Q: The annual per capita share of U.S. total expenditures for heath care (in dollars per year) for…

A:

Q: The projected rate of increase in enrollment in a new college is estimated by dE/dt= ( at+1)^-1(…

A: Given the projected rate of increase in enrollment in a new college is dE/dt= ( at+1)^-1( a+1). We…

Q: 2. A population of birds (in millions) t years from now is estimated by the following P (t) =…

A: Please see the answer below.

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A:

Q: Q2 The rate of heat transfer of a body can be express as: dT -k(T – Ta) dt where T= temperature of…

A:

Q: Alabama Instruments Company has set up a production line to manufacture a new calculator. The rate…

A: Given: dx/dt=4300-4300(190/(t+20)^2)

Q: 2. For time t > 0, a particle moves along the X-axis, its position is given by the function s(t) =…

A:

Q: A company estimates that its revenue grows continuously at a rate given by R'(t)= 2e^2t, where t is…

A: By Using simple integration

Q: A culture initially has P number of bacteria. At t = 3hour the number of bacteria is measured to be…

A:

Q: Find the present value P of a continuous income flow of c(t) dollars per year using c(t)e-rt dt, J-…

A:

Q: The annual per capita share of U.S. total expenditures for heath care (in dollars per year) for…

A:

Q: According to the Florida Agency for Workforce, the monthly average number of unemployment claims in…

A: This question is based on application of Derivative.

Q: A particle moves along the y-axis so that at time t≥0 its position is given by y(t)=t3−6t2+9t. Over…

A: A particle is moving along the y-axis its position is given by y(t)=t3-6t2+9t      at…

Q: Suppose the height of a spacecraft at time 1 is given by f () = 27 E1 for 0 <15 3. Find an…

A:

Q: Because a new employee must learn an assigned task, production will increase with time. Suppose that…

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Q: A company has invested in an online tool that is expected to generate a continuous revenue at a rate…

A: Given that revenue is 252 thousand. And cost is -t2+578t The objective is to find the profit in…

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A:

Q: A moving object has a constant acceleration of -9.8 meters per square second. If its initial…

A:

Q: The acceleration of a particle moving along a horizontal line is given by a(t) = 2t - 2. If particle…

A:

Q: The population of a city (in millions) at time t (in years) is P(t) = 2.1e0.007" , where t = 0 is…

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Q: it is known from experiments that the height (in meter) of a certain plant after t months is given…

A: Given: ht=t-t; 0≤t≤1 for finding given values, first we draw graph of given function on given…

Q: A company has invested in an online tool that is expected to generate a continuous revenue at a rate…

A: Consider the given information:

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A:

Q: Q2 The rate of heat transfer of a body can be express as: dT -k(T – Ta) dt where T= temperature of…

A:

Q: Based on a preliminary report by a geological survey team, it is estimated that a newly discovered…

A: Answer:Given R(t)=800t2t3+32+5  ,  0≤t≤20let n(t) be no. of barallels of…

Q: A small brewery considers the output of its bottling machine as a continuous income stream with an…

A: According to the total income of Continuous Income Stream: If the rate of receipt of revenue is ft…

Q: 3. For time t > 0, a particle moves along the X-axis, its position is given by the function s(t) =…

A: Consider the given position function. st=-t3+3t2-6 Find the double derivative of the position vector…

Q: The marriage rate in a certain country in 1990 was 0.95%, and there were about 351,000 marriages…

A: 1990 corresponds to t=0 So, M0= 351000 And r= 0.95% = 0.0095 So the model is:

Q: (a) If A is the area of a circle with radius r and the circle expands as time passes, find in terms…

A:

Q: (b) If a rock is thrown upwared on the planet mars with a velocity of 12ms, its height in meters t…

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Q: at the rate of r (t) = 3t liters per minute, where t is the time in Which of the following defines a…

A:

Q: A radioactive material went through a decaying process as given in the following function f(t): f(t)…

A: If the input variable t of a function changes, its output also changes. In this problem, the…

Q: Suppose that the rate at which the concentration of a drug in the blood changes with respect to time…

A: Given:The rate of change of concentration of a drug in blood with respect to time t is

Q: With U.S. Census Bureau data (actual and projected) for selected years from 1960 to 2050, the rate…

A: Find the second derivative of P

Q: A mining expert estimates that the production growth rate of copper overtime, or /dt , is given by…

A: We will use method of solving Leibnitz's linear differential equation

Q: to the South Coast Air Quality Management District, the level of nitrogen dioxide, a brown gas that…

A: Here,  A(t)=0.03t3(t-7)4+60.2, 0≤t≤7

Q: The population of a city (in millions) at time t (in years) is P(t) = 2.4e0.007t When will the…

A: find the value of t when population is double from what it is when time is zero.substitute value of…

Q: The population of a culture of bacteria has a growth rate given by p'(t) = 210 bacteria per hour,…

A: Given data is: The population of a bacteria growth culture is: p't=210t+1r  The increase in…

Q: Q2 The rate of heat transfer of a body can be express as: dT = -k(T – Ta) dt where T= temperature of…

A: Using Euler's method we can find the solution, the initial values are t0 = 0 and T0 = 90°C The…

Q: If the position of a particle on the x-axis at time t is-5t", then the average velocity of the…

A:

Q: If s(t) is the position on the x-axis of a particle at time t, then the quantitys(t + h)−s(t) / h…

A: If s(t) is the position on the x-axis of a particle at time t,

Q: A particle moves along the x-axis so that at time t≥0 its position is given by x(t)=2t3+3t2−36t+50.…

A: given, A particle moves along the x-axis so that at time t≥0 its position is given by…

Q: The population of a city (in millions) at time tt (in years) is P(t)=2.7e0.002tP(t)=2.7e0.002t,…

A:

Q: A particle moves along the X-axis so that at time t>0 its position is given by x(t)= 2t3 +…

A:

Q: The population of a city (in millions) at time t (in years) is P(t)=2.8e0.008t, where t=0 is the…

A: Given data:   The expression for the given population at any time t is: P(t)=2.8e0.008t.     The…

Q: The equation y = log(x + 4) has a vertical asymptote at: %3D X =

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.