The rate of change in data entry speed of the average student is  ds/dx = 8(x + 9)−1/2,  where x is the number of lessons the student has had and s is in entries per minute. (a) Find the data entry speed as a function of the number of lessons if the average student can complete 48 entries per minute with no lessons  (x = 0).

Q: The time rate of change of an alligator population P in a swamp is proportional to the square of P.…

A:

Q: The growth rate of Escherichia coli, a common bacterium found in the human intestine, is…

A: a: it doubles in every 30 minute and initial population = 10 then we can write the function as:…

Q: In the equation, x2+y2=45, what is the value of the rate of change in y with respect to the time t…

A: Given : x2 + y2 = 45dxdt = -2x = 3

Q: A culture contains 1400 bacteria initially and doubles every 50 minutes. Assuming that the rate of…

A: Consider the function that models the number Pt=Aekt=B2tC Here, the objective is to find the…

Q: Find the 1st and 2nd derivative of this function: x=(t-2)5/2  y=t3-5

A: We will differentiate the function twice to get the first and second derivatives as follows while…

Q: Q4:- Construct the following mathematical models :- 1) The time rate of change of a population P is…

A: See the attachment

Q: d 3) (2a)* = (Derivative of an exponential %3D function)

A:

Q: Because of job outsourcing, a town predicts that its public school population will decrease at the…

A: Proceed as shown below...

Q: 2. Informally explain that a function is considered differentiable, if small changes dx, to the…

A:

Q: Find the absolute extrema of the function f(x) = (x + 16) 1/3 on the interval[-5,2]. Find the second…

A: To find  The absolute extremum of the given function.

Q: The rate of growth of profit (in millions) from an invention is approximated by P'(x) =xe x, where x…

A:

Q: What is the rate of change for h(x) = 8x - 9 on the interval [1, 4]?

A:

Q: 8) A company's demand equation is x - V 2000 - p² , where p is the price in dollars. Find dp/dx when…

A:

Q: The growth rate of Escherichia coli, a common bacterium found in the human intestine, is…

A: (a) Given: The initial population is 500. The number of cells in a culture doubles approximately…

Q: y = (e*+4 +2)/(e2+3x +1)

A: y=e-3x+4+2e2+3x+1

Q: Find the instantaneous rate of change for the function at the given value. f(x) =x + 4x at x= - 4…

A: NOTE: Refresh your page if you can't see any equations. . to find the instantaneous rate of change,…

Q: Find the first and second derivative of this function: x=(t-2)5/2  y=t3-5

A: We have to find derivative

Q: The rate of growth of the bacterial population is proportional to the number of bacteria present at…

A: Introduction: Differential Equation applications are useful in both the classroom and in real life.…

Q: The marginal cost of serving a typical additional client at a law firm can be modeled by dC 675…

A: Given Data The equation of the marginal cost is dC//dx=675-0.5x.   Integrate the equation of…

Q: In the manufacture of printing ink, solvents are used to suspend or dissolve the pigments that give…

A:

Q: Find the instantaneous rate of change for the function at the given value. f(x) =x+3x at x= - 1 The…

A:

Q: Find a real number a such that the instantaneous rate of change of the function flx) =2x²+ 4x+7 at x…

A:

Q: A colony of fruit flies grows at a rate proportional to its size. At time t = 0, approximately 20…

A: Let the population of fruit flies be modelled by function y.  The question mentions that the rate is…

Q: 14. Find the rate of change of y= (2x' +6x +4) at x =-1.

A:

Q: The concentration of an antihistamine in the bloodstream of a healthy adult is modeled by C = 12.5 -…

A:

Q: The concentration of an antihista-mine in the bloodstream of a healthy adult is modeled by C = 12.5…

A: 6 hour period means from t=0 to t=6That is from start of the medication  to 6 hours after medication…

Q: A linear model of the spread of an epidemic in a community of 1000 people is the equation: dx/dt =…

A: To find the number of people x(t) who have contracted the disease at the time oftime t.

Q: A smokestack deposits soot on the ground with a concentration inversely proportional to the square…

A:

Q: Find the marginal profit for producing x units. ( P = -0.3x³ + 10x² – 168.45x - 3000 dP dollars per…

A: Marginal profit is the measure of the increment of the profit function for unit increment of x, at a…

Q: Use differentials to approximate the change in profit corresponding to an increase in sales (or…

A:

Q: A factory is dumping pollutants into a river at a rate given by dx/dt = t3/4/600 tons per week,…

A: First we separate the variables

Q: The number of bacteria in a liquid culture is observed to grow at a rate proportional to the number…

A: We know that at the beginning of the experiment, number of cells = 104 After 3 hours of the…

Q: A factory is dumping pollutants into a river at a rate given by dx/dt=t3/4/400 tons per week, where…

A: Given that A factory is dumping pollutants into a river at a rate dxdt=t34400

Q: IfI represents the intensity of light which has penetrated water to a depth of x feet, then the rate…

A:

Q: The amount of photosynthesis that takes place in a certain plant depends on the intensity of light x…

A: Given fuction

Q: The rate of U.S. per capita sales of bottled water for the period 2000-2010 can be approximated by…

A:

Q: 7 Since the development of the iPod, the stock price of Apple has been growing rapidly and has been…

A: Given that the stock price of Apple has been growing rapidly using equation y=3.2e0.5x We compare…

Q: 10. Solve for the derivative of y IMPLICITLY 22 + Væ³ + 2y= y²

A: Note: According to our expert guidelines only first individual question is to be answered, kindly…

Q: In the manufacture of printing ink, solvents are used to suspend or dissolve the pigments that give…

A: Rt=10t5t2+4

Q: The growth rate of Escherichia coli, a common bacterium found in the human intestine, is…

A: Given The number of cells doubles every 30 minutes. A) Initial Population =1000 B) Initial…

Q: The monthly output of a certain product isQ(x) = 2400x5/2where x is the capital investment in…

A: The monthly output of a certain product is Q(x) = 2,400x5/2, where x is the capital investment in…

Q: A5.5-foot-tall woman walks at 4 ft/s toward a street light that is 16,5 ft above the ground, What is…

A:

Q: A new computer costs $2000 today and decreases in value at a constant rate of $500 per year. Denote…

A:

Q: A bucket that weighs 3 lb and a rope of negligible weight are used to draw water from a well thatís…

A: weight of bucket=3lb weight of water at starting=37lb deepness of the well =60 feet bucket lifts at…

Q: The rate of growth of a fish population was modeled by the equation G(t) =…

A: Consider the given: Gt=90000e−0.6t1+5e−0.6t2

Q: In an autocatalytic chemical reaction, the product form is a catalyst for the reaction. If Qo is the…

A:

Q: The cost in pesos of producing x units of a certain commodity is C(x) = 0.05x2 + 10x + 5000. What is…

A:

Q: Find the instantaneous rate of change for the function at the given value. f(x) = x² + 3x at x = 0…

A: We can find the instantaneous rate of change as below

Q: The instantaneous rate of change for the function Y=x^2+2x,  at x= 3

A: The rate of change of any function is given by dydx  at any point x=x0 ,that is derivative of 'y'…

Q: A culture contains 2000 bacteria initially and doubles every 40 minutes. Assuming that the rate of…

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.