A manufacture of compressed gasses is looking at new legislation that would require it to reduce the amount of pollution it produces. The cost C, in dollars, of removing p percent of the particulate pollution from the exhaust is 9300p Let C(p) 100 – p - Then C' (p) =

A manufacture of compressed gasses is looking at new legislation that would require it to reduce the amount of pollution it produces. The cost C, in dollars, of removing p percent of the particulate pollution from the exhaust is 9300p Let C(p) 100 – p - Then C' (p) =

Algebra for College Students

10th Edition

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter10: Exponential And Logarithmic Functions

Section10.2: Applications Of Exponential Functions

Problem 47PS

See similar textbooks

Related questions

Q: an integrating factor for the DE dy+ydx=e3x dx is 1)ex 2)x2 3)y 4)x 5)ey

A: To find an integrating factor for the DE dy+ydx=e3x dx

Q: Solve the follow ing initial value problem: 3x(t2- 1)dt+ (t³ + 8x- 3t)dx= 0, t(0)= 1

Q: Solve the differendialegimaition: (2x+e)dx + (xay co

A: Make some simplification and rearrange the given differential in exact form.

Q: If P0 is the initial population at t = 0 and k depends on the rate of growth, then the formula for…

A: Given, P0 is the initial population at t = 0 and k depends on the rate of growth Population usually…

Q: Give an example of birthrates Ai >0 such that a birth process (Xt)t>0 with birthrates di, i20…

A: The example of birthrates should follow Poisson's distribution where λi are the birthrates, since…

Q: Solve the initial-value problem. dy for x21 with y(4) = 4 %3D dx The solution to the initial-value…

A: We have to solve the initial-value problem: dydx=5x Solving by variable separable method,…

Q: Solve the initial-value problem for y as a function of x. (16 – x)- dy = 1, y(0) = 5 dx ((1 - D- -…

Q: Given y=5x+2−−−−−√, find the differential dy when x=1 and dx=0.3. Round your answer to three…

Q: 4 solve the D.E " -X² Joly =0 3x2 ydx + LY

Q: Solve the initial-value problem for x as a function of t . dx (2t3 – 2t? + t – 1)- = 3, x(2) = 0 dt

Q: Show if the the initial value problem is dy separable or not -=y²(1+x²) • dx vith the initial value…

Q: f(x, y) = log, (3x) fe dy In(3x)/(yln(y)2)^2 ||

A: Topic- partial differential

Q: d Q. S Vt In(t)dt equals dx a. 4x³ (In x) – /2 ln(2) b. 4x5 (ln x) – /2 ln(2) c.4x³ (ln x) d. 16x°…

Q: a) A capacitor (C) which is connected with a resistor (R) is being charged by supplying the constant…

A: Given : E = ∫0∞P(t) dt , P(t) = 5Re-tRC2×R

Q: A clamped beam of length 3 is modeled by: y(4) = 24, y(0) = y'(0) = 0, y(3) = y'(3) = 0. Solve the…

A: The given differential equation is y4=24, with y0=y'0=0 and y3=y'3=0 Now we integrate the given…

Q: Solve the initial value problem for y as a function of x. x2 - 16 dy = X, x > 4, y(8) = 0 dx

Q: Solve the initial value problems for y as a functionof x. (x2 + 4) dy/dx = 3, y(2) = 0

A: Given Data : Differential Equation x2+4dydx=3, y2=0 1 The given initial value…

Q: Obtain the General Solution (x-1 )dx - (3 x -2y -S) dy = 0 MAM

Q: for t> -1 with y(0) = 11. y =

A: First we find Integrating factor then we find solution.

Q: Find the Bolution to Hhe initial value problem - Please Write the folution with the computer.

A: Solution of Linear Differential Equation with Constant Coefficients: The general form of linear…

Q: Solve the initial value problem. dx dt -4tx=t Int+3, x(1) = 0

Q: Jesaki Inc will sell N units of product after spending $x thousand in advertising, as given by N =…

Q: Solve the initial value problem dz/dt=cost−2sint, z(0)=5.

Q: Solve the initial-value problem. dy for x20 with y(0) = 2 5 dx The solution to the initial-value…

Q: 1. e-st cosh t dt 2x +4 2. 2x2 + 21x + 34

Q: Solve the initial-value problem for yy as a function of x. (x2+49)dy/dx=1,y(7)=0.

Q: A useful new product is introduced into an isolated fixed population of 1,000,000 people, and 100 of…

A: If x denotes the number of people who adopted the product at time t, measured in then we have the…

Q: An integrating factor which convert the D. E. y p(y)dx – (Qly) – p)x)dy = 0, into exact is given by

Q: (1² +21) dx dt = = 2x + 2 (t, x > 0), x(1) = 1

A: Given that: t2+2tdxdt=2x+2 ; x(1)=1. Find the solution of this initial value problem.

Q: The number N(t) of supermarkets throughout the country that are using a computerized checkout system…

A: The number N(t) of supermarkets throughout the country that are using a computerized checkout system…

Q: Solve the initial-value problem for x as a function of t . dx (2t3 – 2t? + t – 1) - 3, г (2) — 0 dt

Q: Find Solution of the Attached ?

A: Given differential equation is 3xy'-y=lnx+1 and y1=-2. Given differential equation can be written in…

Q: The size of a population x as a function of time y is given by dx/dy=0.02x+9y . Solve for x as a…

Q: dy Solve the initial – value problem: = y² given that f(0) = -1 dx %3D

Q: Solve the initial value problems for x as a functionof t. (t2 + 2t) dx/dt = 2x + 2 (t, x > 0),…

A: t2+2tdxdt=2x+2⇒dx2x+2=dtt2+2t Now integrating on both sides, we get…

Q: Find the particular antiderivative of the function f(x) = e"(2" – 1) whose graph passes through the…

A: Integration

Q: (a) Integrate x ln(x + 1)dx analytically; and numerically using (b) trapezoidal rule with iterations…

A: As per the rules we can solve only 3subparts per questions so I'm solving a,b,c

Q: Jesaki Inc will sellN units of product after spending $a thousand in advertising, as given by N = 73…

Q: Solve the initial value problems for y as a functionof x. (x2 + 1)2 dy/dx = √x2 + 1, y(0) = 1

A: x2+12dydx=x2+1⇒dydx=x2+1x2+12⇒dydx=1x2+132⇒dy=1x2+132 dx Now integrating on both sides, we get…

Q: Solve the initial value problems for x as a functionof t. (t2 - 3t + 2) dx/dt = 1 (t > 2), x(3) =…

A: Solution: Consider the given initial value problem is t2-3t+2dxdt = 1 (t>2) Now, separating the…

Q: Find the differential dy of the given function. (LUse "cx" for dx.) x +3 3x

A: We will solve the problem

Q: The integrating factor of the given DE are already given below. What is the value of "n" yly²-x-8)dx…

Q: Solve the initial-value problem for x as a function of t. (2t³ − 2t² + t − 1) = 0 dx dt = 3, x(2) =

Q: Find the total differential df to the function f(x, y) = x²y – xy? when x decreases from -2 to -2.01…

A: We will find out the required value.

Q: solve the initial value problem dx/dt=x-x^{3} with x(0)=1 Please provide valid answer

A: Given differential equation is

Q: In x Find y' if y = e3 1 – 4 In x Based on your work from (a), evaluate - dx. -5

Q: Solve the initial-value problem for y as a function of x. (25−x^2)dy/dx=1, y(0)=9 y=?

Q: solve the initial value problem dx/dt= x-x^3 with x(0)=x0

A: From the given statement, the initial value problem dx/dt =x – x3 with x (0) = x0.

Concept explainers

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.

Question

A manufacture of compressed gasses is looking at
new legislation that would require it to reduce the
amount of pollution it produces. The cost C, in
dollars, of removing p percent of the particulate
pollution from the exhaust is
9300p
Let C(p) = (-
100 – p
Then C' (p) =

Expert Solution

Step 1

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differential Equation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

A manufacturing company has been experimenting with a new additive that is used to reduce polluting effluents from its production facility. Test results suggest that if no additive is used, pollution levels are 3000 parts per million (ppm). For each pound of additive used per week, pollution levels are reduced by 0.49 ppm. The additive costs $30 per pound. The reason for experimenting with the additive is that a government agency is conducting weekly air quality tests in the vicinity of the production facility. Regulations state that if pollution levels exceed 2000 ppm, a fine is imposed. The fine is $1000 for each ppm by which the pollution level exceeds the 2000 ppm limit. If the company has budgeted $80,000 per week to spend on the additive and any pollution fines, how much additive should be purchased each week for use by the company? What is the resulting amount that the company is willing to pay in terms of weekly fines?
Total net shipments of aluminum (in billions of pounds) are approximated by g(x) = 16.2 + 2.86 In(x + 1) where x=0 corresponds to year 1990 a) How many pounds of aluminum were sipped in 2004? b) Assuming the continued accuracy of the model, when will aluminum shipments reach 27,400,000,000 pounds?
The population of the city of Bingville increases at a rate proportional to the numbers of itsinhabitants present at any time t. If the population of Bingville was 30,000 in 1970 and 35,000 in1980, what will be the population of Bingville in 1990?
11.Suppose that during a controlled experiment, the temperature in a test tube attime t is rising at a rate of 6t^2+2 degrees centigrade per minute. If the initialtemperature is 20°C, what is the temperature in the test tube after 10 minutes?
With more offspring produced in age class 1 (x = 1), the patient population could match the rate of population growth rate of the speedy population. By trial and error, approximate the number of offspring (1 decimal place) that must be produced in age class 1 of the patient population such that the growth rates of the two populations are almost identical.
The management at a certain factory has found that the maximum number of units a worker can produce in a day is 75. The rate of increase in the number of units N produced with respect to time t in days by a new employee is proportional to 75 − N.
For the production function Q (K,L)= 1000 (KL3 )1/3 , Given the current input level K = 400 and L = 40. Use marginal analysis to estimate the approximate change in output which results form an increase in K of 9 units and a decrease in L of 7 units. Verify that Young′s Theorem holds?
An editorial in the New York Times on Sunday June 4, 2011 dicussed the redesigned fuel economy stickers to be required on new cars starting in 2013. Consider a new idsize fuord fusion s model. At $4-a-gallon gas, annual fuel costs would be about $2,200 for 15,000 miles driven... And thats for a car with a rated mileage of 34.9m.p.g. actual highway mileage, as with all vehicles, is lower, in this case about 27m.p.g. Industry clearly needs to do better. Did the times use the rated or the actual mileage in its computation?
A cultureinitially has No numberof bacteria. At t = 1, time in hour, the numberofbacteria is measured to be 1/2No.If the rate of growth is proportional to the numberof bacteria N(t) present at time t, determine the time necessary for the number ofbacteria to triple.
Under certain conditions, cane sugar with water is converted into dextrose at a rate which is proportional to the amount unconverted at any time t. If initially there was 75 grams of cane sugar with water and that 8 grams are converted during the first 30 minutes, find (a) the amount converted in 1.5 hours, in grams; (b) the time at which 99% of sugar cane with water had been converted to dextrose.
Suppose that a community contains 15,000 people who are susceptible to Michaud’s syndrome, a contagious disease. At time t = 0 the number N(t)of people who have developed Michaud’s syndrome is 5000 and is increasingat the rate of 500 per day. Assume that N0 t is proportional to the product of the numbers of those who have caught the disease and of those who have not. How long will it take for another 5000 people to develop Michaud’ssyndrome?
The City Council proposed to utilize government-owned land with an area of 9,600 square meters. One-third of the area will be used to plant mango trees while the rest of the land is where an emergency field hospital shall be built. As the city engineer, you were tasked to determine the rate at which the total average number of COVID cases is increasing at x=10 tents and dx/dt=1 tent per day, given that if 30 tents are built, the average number of COVID cases per tent will be 7 cases while the average number of cases will increase by 2 per tent for each additional tent in the same area due to overcrowding.