PROBLEM 2: The profit of a company is given by the function below, where P is the profit and n is the number of sales. Calculate the percent change in profit as sales increase from 115 to 120 units using differentials. P = 100xe¬x/400

Q: In Example 6 in this section, we were given f(x) = 3x2 + 2x + 11 and found f '(x) = 6x + 2. (a)Find…

A: We have to given that f(x)=3x2+2x+11 and f'(x)=6x+2. It is known that rate of change is given as…

Q: Problem 2 dA (a) If A is the area of a circle with radius r and the circle expands as time passes,…

A: Given that, Suppose oilspills from a ruptured tanker and spreads in a circularpattern. If the radius…

Q: Solve the following problems completely. 1. If a body whose temperature is initially 200° C is…

A: Use Newton's law of cooling

Q: QUESTION 15 An accessories company finds that the cost, in dollars, of producing x belts is given by…

A: Given : cost in dollars when producing x belts

Q: Problem #2 One airplane is approaching an airport from the north at 199 km/hr. A second airplane…

A: We have to find the rate at which distance between the planes is changing.   According to our…

Q: Problem 4: Given the function /(x) = 4x -x+1. (a) Find the average rate of change of f(x) with…

A: We have to find the average rate of change of the function fx=4x2-x+1 with respect to x over the…

Q: If the population (in millions) of a country as a function of time (in years) is P(t) = 10 · 2kt,…

A:

Q: Question 1. Find the average rate of change of the function f(x) = x² – 5 on the interval [2, 2 +…

A: WE HAVE TO FIND THE AVERAGE RATE OF CHANGE OF A FUNCTION   given function is f(x)=x2-5   Given…

Q: Problem 3. Two boats are racing with constant speed toward a finish marker, boat A sailing from the…

A: Given : Boat A is sailing from south at 13 mph and boat B is approaching from the east.

Q: PROBLEM: C Suppose a ball is dropped from a height of 4900 feet. Its position at time t is s(t)…

A:

Q: A car traveling at the rate of 20m/s is approaching an intersection. When the car is 100 meters from…

A: Given: dadt=20 m/s and   dbdt=100m/s at   t=2 sec first we convert m into ft so, 20m/s×3.281=65.62…

Q: TASK 02 Part A The rate of change of a population of bacteria in a petri-dish can be described as…

A: Given: The rate of change of a population of bacteria in a petri-dish can be described as the…

Q: The gross domestic product (GDP) of a certain country is projected to  be N(t) = t2 + 2t + 50 ( 0 ≤…

A:

Q: Problem 4. Suppose that a firm's capital and labour vary in time as follows: k(t) = 2t², 1(t) = 2t +…

A:

Q: Problem. 3: The population of a city is increasing at a rate directly proportional to the population…

A: integration method

Q: The population of a town is given by the formula: P(t) = 1000e^(.02t), where t is in years. What is…

A: Given: Pt=1000e.02t

Q: Problem. 16: Gator Golf Cartz has determined that it takes r units of labor and y units of capital…

A:

Q: PROBLEM [ B4 ]: Two resistors R1 and R2 are connected in parallel in an electric circuit. If the…

A: We have to find the absolute change , relative change and percentage change .

Q: Problem #2: The sales of a plastic widget were estimated to be: P(t) = 8000 t e-0.6t where t is in…

A: To compute the total number widgets sold, use the definite integral. Here, the variable t varies…

Q: I. SOLVE THE FOLLOWING PROBLEMS. 1. A silver bullet used to kill vampires in the late 19th century…

A: Given that: Temperature of silver bullet cools from 100°C to 90°C in 5 mins.                    and…

Q: Using U.S. Energy Information Administration data for selected years from 2010 and projected to…

A:

Q: Problem 7. The population in California P(t) (in millions) can be approximated by the logistic…

A: Given population expression is  P(t)=95.2/{1+1.8e-0.018t}

Q: Problem 5 A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine…

A: To determine the final concentration of the salt in the solution, we have to first determine the…

Q: Problem. 2: The world population at the beginning of 1980 was 4.5 billion. Assuming the population…

A:

Q: If the rate of change of Q is inversely proportional to Q (where Q > 0), and if Q(0) = 250 and Q(2)…

A: Given rate of change of Q is inversely proportional to Q. We need to find the proportionality…

Q: It is estimated that x months from now, the population of a certain town will be changing at a rate…

A:

Q: Problem 4 The temperature (0) of a hot spherical ball that is cooling changes as a function of time…

A: Given Differential equation for the temperature of a hot spherical ball that is cooling changes as…

Q: Given a function f(x)=e^2x−e^x+1, what value of x makes the relative rate of change equal to one?

A: We first find f'(x) using chain rule f(x)=e2x−ex+1f'(x)=2e2x-ex

Q: Question 9 ( :) The demand for nurses in the US between 2000 and 2015 is estimated to be: D(t) =…

A: The demand of nurses in the US between 2000 and 2015 is estimates to be in form of a demand equation…

Q: Problem 3. The rate of consumption of hamburgers in Wyoming (in millions of hamburgers per year)…

A:

Q: Problem 5. Let A and k be positive constants. Which of the given functions is a solution to = k(y +…

A: Given: dydt=k(y+A) A and K is positive constant

Q: Question 26 Calculate the average rate of change for the function f(x) = 2x² − 3x + 5 1 over the…

A:

Q: QUESTION 4 Let C(x)=.0051x3+1.78x2+24000 represent the cost of producing X units of a good. Answer…

A:

Q: Problem 1: A mass m is accelerated by a time-varying force exp(-ßt)v, where v is its velocity. It…

A: Please check step 2 for the solution of problem 1.

Q: EXAMPLE 3 Suppose that a ball is dropped from the upper observation deck of the CN Tower in Toronto,…

A: Given data:The distance after 't' second is St=4.9 t2

Q: PROBLEM 6: The measurement of a side of a square is found to be 12 cm, with possible error of 0.05…

A:

Q: Problem. 1: Under ideal laboratory conditions the rate of growth of bacteria is proportional to the…

A: At the end of 5 hours = 21,000

Q: Question 7. A manufacturer of jet engines estimates that the rate at which maintainance costs are…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Problem 3 A par ticle is moving along a line with acceleration function (in meters per second…

A: We have  a = 2t +3

Q: QUESTION 2 Estimate the value of V80.9 + V80.9 using differentials.

A: To evaluate : 80.94 +180.94 Let f(x) = x14 Now, we can write 80.9 = 81- 0.1 Take x=81, ∆x=-0.1

Q: PROBLEM 1: A bacteria culture has an initial population of 500. After 4 hours, the population has…

A:

Q: Estimate 5JL 1.01 using linearization

A: Consider  1.015

Q: if f=5 is an equilibrium solution of an equation of change involving df/dx, what is the value of…

A: f=5 is an equilibrium solution of an equation of change involving dfdx.

Q: Problem 2. The population of a certain city is projected to grow at the rate of (1+ 26) (0sts6) r(t)…

A:

Q: 1. Problem 1 (a) Differentiate V3x 6+ x* (b) Differentiate f (x) = (ax³ + b)(cr² + d) (c) The…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Find the rate of change of total profit, in dollars, with respect to time where R(x)=80x−0.5x2 and…

A:

Q: Problem [4] Factory is polluting a lake in such a way that rate of pollutant (population) entering…

A: This question is related to definite integration, We will solve it using given information.