75p %3D where C is the cost The cost to remove a toxin from a lake is modeled by the function C(p) 85 P - (in thousands of dollars) and p is the amount of toxin in a small lake (measured in parts per billion [ppb]). This model is valid only when the amount of toxin is less than 85 ppb. a. Find the cost in dollars to remove 45 ppb of the toxin from the lake. C = $ (round to the nearest whole dollar) b. Find the formula for the inverse function. p = f(C) = c. Use part b. to determine how much toxin is removed for $40,000. ppb (round to 2 decimal places)

Q: A foul tip of a baseball is hit straight upward from a height of 4 feet with an initial velocity of…

A: Given function is, s(t)=-16t2+96t+4

Q: NASA launches a rocket at t=0t=0 seconds. Its height, in meters above sea-level, as a function of…

A: NASA launches a rocket at t=0 seconds. Its height, in meters above sea-level, as a function of time…

Q: A ball is thrown straight up from ground level with an initial velocity of 96 feet per second. The…

A: Given: st=-16t2+96t We know that for given position functionst, velocity functionvt is given by…

Q: A large mixing tank currently contains 50 gallons of water into which 5 pounds of sugar have been…

A: Here the concentration will be represented in pounds per gallon

Q: NASA launches a rocket at t = seconds. Its height, in meters above sea-level, as a function of time…

A:

Q: 3. Use the function g(x) = 2x- 3 to fill in the table below and graph. %3D a) What type of function…

A: Domain set of all input values where f defined Range set of all output values

Q: A forest fire leaves behind an area of grass burned in an expanding circular pattern. If the radius…

A:

Q: After consumption of an alcoholic beverage, the concentration of alcohol in the bloodstream surges…

A:

Q: The rate of change in data entry speed of a student is ds/dx = 7(x + 1)−1/2, where x is the number…

A:

Q: The figure shows water running into a container in the shape of a cone. The radius of the cone is 6…

A:

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

A:

Q: A car rental agency charges $200 per week plus $0.15 per mile to rent a car. a. Express the weekly…

A: It is given that,   Fixed charges per week is = $200  Charges for per mile is = $0.15     Now by…

Q: NASA launches a rocket at t = 0 seconds. Its height, in meters above sea-level, as a function of…

A:

Q: Carrie, marine biologist is performing experiments along the continental slope off of the coast of…

A: Now the speed of the current at the depth of the robot as a function of time is,

Q: You record the temperature every hour from midnight until​ 8:00a.m. You see that the temperatures​…

A:

Q: The number of bacteria in a culture is modelled by the function n(t) = 500 e 0.45t, where t is…

A:

Q: The amount of a pollutant (measured as parts per million) in a local lake can be modeled by the…

A: ∗Given:-       Amount  of   pollutant,       At=14×2.71-0.016 t ‐‐‐i∗ To  find:-        Time  taken…

Q: An explosion causes debris to rise vertically with an initial velocity of 72 feet per second. The…

A: Given: st=-16t2+72t derivative of s at a is defined as s'a=limh→0sa+h-sah substitute a+h for t in…

Q: The rate of change in data entry speed of a student is ds/dx = 9(x + 1)-1/2, where x is the number…

A: To determinePart a) The data entry speed as a function of the number of lessons the student has…

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

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

Q: The demand for a certain commodity is -05x D(x) = 6000e %3D units per month when the market price is…

A: To find out the rate of consumer expenditure.

Q: Although primarily used for relief of pain, opioids have addictive properties that often make…

A:

Q: The concentration of a drug in the bloodtream t minutes after the injection is modeled by the…

A: Given   We need to find the time when maximum concentration occurs

Q: For some positive constant C, a patient's temperature change, T, due to a dose, D, of a drug is…

A: To find the solution

Q: The concentration C of a drug in a patient's bloodstream t hours after injection is given by 25 · t…

A:

Q: The half-life of chemical substance is approximately 6 years. Initially there is 40 grams of the…

A:

Q: Park rangers introduce 50 elk into a wildlife preserve. The function 250(3t + 5) f(t) = t + 25…

A: Given that, The function of population is f(t)=2503t+5t+25

Q: The rate of change in data entry speed of the average student is ds/dx = 7(x + 9)-1/2, where x is…

A: The given equation is a differential equation. Hence the solution of the differential equation…

Q: The position of a particle moving along the x-axis at any time t is modeled by the function s(t) =…

A:

Q: NASA launches a rocket at t = 0 seconds. Its height, in meters above sea-level, as a function of…

A:

Q: The rate of change in data entry speed of the average student is ds/dx = 4(x + 1)¬1/2, where x is…

A: Given: The rate of change in data entry speed of the average student is dsdx=4(x+1)-12 Now,…

Q: The concentration C in milligrams per milliliter​ (mg/ml) of a certain drug in a​ person's…

A:

Q: The rate of change in data entry speed of the average student is ds/dx = 7(x + 9)-1/2, where x is…

A:

Q: At the surface of the ocean, the water pressure is the sameas the air pressure above the water, 15…

A: Given: At the surface of the ocean, the water pressure is the same as the air pressure above the…

Q: A large koi pond is filled from a garden hose at the rate of 19 gal/min. Initially, the pond…

A:

Q: The concentration C in milligrams per milliliter​ (mg/ml) of a certain drug in a​ person's…

A:

Q: The rate of change in data entry speed of the average student is ds/dx = 6(x + 4)-1/2, where x is…

A:

Q: Price-demand. Suppose that the daily demand (in pounds) for chocolate candy at $x per pound is given…

A: Given demand function is D=1000-40x2 ,    1≤x≤5 Here 'x' represent price (in dollars) of per pound.

Q: . (a) Compare the rates of growth of the functions f(x) = 3* and g(x) = x* by drawing the graphs of…

A: (a) Given information: fx=3xgx=x4

Q: 2. The population of deer after t years in Cedar State Park is modeled by the function P(t) = 1001/(…

A:

Q: The cube root parent function y = Va has been transformed. What is the equation of the new image? -5…

A:

Q: The number of students infected with flu at a high school after t days is modeled 700 by the…

A:

Q: 3. The perimeter of a rectangle is 40 in. Find a mathematical model expressing its area A as a…

A: Let l and b be the length and breadth of the rectangle respectively. The perimeter of the rectangle…

Q: The initial size of a culture of bacteria was 200. After 30 minutes, the count is 450. a) Find the…

A: We will solve this using both models given

Q: NASA launches a rocket at t is given by h(t) = - 4.9t + 46t + 283. O seconds. Its height, in meters…

A:

Q: The total cost of manufacturing x units  during the daily production run  at a factory, is C(x) = x2…

A: Given:

Q: 6. The function f(x) = 4x + 10 models the amount of money Francis makes when babysitting for x…

A:

Q: The rate of change in data entry speed of the average student is ds/dx = 6(x + 9)¬1/2, where x is…

A: Rate of change in data entry speed of the average student is given in the problem, so to find a…

Q: The deeper you are under water; the less sunlight reaches you. The percent of sunlight, P, that…

A:

Q: a) Express the mathematical function between the variables h and r shown in the figure. b) How fast…

A: The water drains from the conical tank at a rate of 0.2 m3 per minute. Let consider at any instant…

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.