The rate of change in data entry speed of a student is ds/dx = 9(x + 1)-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 student can complete 22 entries per minute with no lessons (x = 0). s(x) : (b) How many entries per minute can the student complete after 48 lessons?

Q: If an amount Po is invested in the Mandelbrot Bond Fund and interest is compounded continuously at…

A:

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

A:

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

A: (b)

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

A: Given a function of amount of photosenthesis taken place in terms of intensity of light x as shown…

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: f(x)=x2+2 find average rate of change from -2 to 0 feom 1-3 and from -1 to 2

A:

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: 3r²+7x What is the first derivative of f(x) = ln|

A:

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: Find the first Derivative complete solution. r= (3cot42θ-4)2/3

A:

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

A:

Q: (2+3t2 3x2 dx 1+ x3 6. Find the derivative of the function F(t) = 2-3t2

A:

Q: The function represents the rate of flow of money in dollars per year. Assume a 10-year period and…

A: Given that,  function f(x) = 0.03 x + 400 Rate r = 8 %  = 0.08 Time period is of 10 years. So time…

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: An epidemic is spreading at the rate of 18e0.2t new cases per day, where t is the number of days…

A:

Q: World consumption of lead is running at the rate of 4.7e0or million metric tons per year, where t is…

A:

Q: a). A drug in the blood stream decays by according to the equation y'=ky, where y is the…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

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: The number of traffic accidents per year in a city of population p is predicted to be T 0.002p ³/2.…

A:

Q: If an amount Po is invested in the Mandelbrot Bond Fund and interest is compounded continuously at…

A: Question- If an amount Po is invested in the Mandelbrot Bond Fund and interest is compounded…

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: A culture contains 2000 bacteria initially and doubles every 60 minutes. Assuming that the rate of…

A: To determine the counting function P(t) explicitly, under the given conditions

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: determine the instantaneous rate of change at x = 2 for f(x) = 5x2 + 3x + 7

A: Topic :- Differentiation

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: An average young person in the United States gains weight at the rate of 16(x - 10)-1/2 pounds per…

A:

Q: Find the 3rd derivative of the function y=f(x) given by the equation x2−y2=9. Solution.

A:

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: Q2: A) Find an equation of the line tangent to the function of x2 + (y- x)² = 9 at x = 1. dy if y =…

A: Derivative of function

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

A:

Q: 13. Snow falls during a storm at a rate of t(4–t) inches per hour, as a function of time t in hours.…

A:

Q: The monthly output at the Olek Carpet Mill is Q(x) = 15,000 + 2x2 units,    (40 ≤ x ≤ 60) where x…

A: Given that the monthly output is Qx=15,000+2x2 units, where x is the number of workers. Find Q'52.

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

A: Please see the explanation below

Q: find the function that gives the value of the investment as a function of t. (Round your value of k…

A:

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

A:

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

A:

Q: When the interest on an investment is compounded continuously, the investment grows at a rate that…

A:

Q: Breathing is cyclic and a full respiratory cycle from the beginning of inhalation to the end of…

A: Given query is to find the volue at time t