A retail store estimates that weekly sales s and weekly advertising costs x (both in dollars) are related by s= 50,000 - 40,000 e 0.0004x The current weekly advertising costs are $2,500, and these costs are increasing at a rate of $300 per week. Find the current rate of change of sales. The current rate of change of sales is s per week. Round to the nearest dollar as needed.)

Q: dE The rate at which a machine operator's efficiency, E (expressed as a percentage), changes with…

A: Integrating dE/dt we get E(t)

Q: The rate at which an assembly line worker's efficiency E (expressed as a percent) changes with…

A: The rate at which an assembly line worker's efficiency E changes w.r.t. time t is given by…

Q: Q1. In a study of Bacterial Growth, it is assumed that, a culture initially has Po number of…

A: P0 → initially number of bacteria.at t= 2h, number of bacteria→52P0We can model the problem as :P(t)…

Q: H(t) models the rate of hoverboard sales, in hoverboards per day, from an electronics store during…

A: H(t) is the rate of hoverboard sales, in hoverboards per day. To get the exact number of sales over…

Q: The rate at which a company produces waste, W, in tons per month, is approximated by W = 3.75e¬0.17,…

A: Given: The rate at which a company produces waste W in tons per month is approximated by…

Q: (B) Use the four-step process to find R'(x). (C) Find the revenue and the instantaneous rate of…

A:

Q: The Body Mass Index (BMI) is a rate of a person's weight in kg divided by their height in meters…

A: Let's find.

Q: s. Two boats leave a port at the same time. One travels west at the speed 20 miles per hour and the…

A:

Q: A new building that costs $1,000,000 has a useful life of 100 years and a scrap value of $200,000.…

A: Initial time = t=0  Final time = 100 years So the points are (0, 1000000) and (100, 200000) Then we…

Q: According to the Florida Agency for Workforce, the monthly average number of unemployment claims in…

A:

Q: Q1. In a study of Bacterial Growth, it is assumed that, a culture initially has Po number of…

A: This is Separable differential question

Q: The time variation of the price C of a particular material is described by the equation C = 5t In(t)…

A:

Q: For a certain square, the side is increasing at the rate of 2 mm/s. At what rate is the perimeter of…

A: We know       Perimeter (P) = 4 × ( side of square)

Q: The area, A, in square metres, of a circular oil spill after t min is given by A = pt2. P=3.14 The…

A: Given that The are of the circular spill after t minutes, A=pt2 , p =3.14 We have find the rate of…

Q: second. Consider the relationship between Jose's distance d east of the mailbox (in feet) in terms…

A: Given that the speed of Jose.  And we know that speed = change is distance / change in time put and…

Q: A country's share of medals at an Olympic games can be estimated from the formula: f(r, y) = 0.0062…

A: Given function is , fx,y=0.0062Inx+0.0064 Iny-0.0652⋯⋯(1) In the given relation, the function fx,y…

Q: A highway patrol plane flies 3 mi above a level, straight road at a steady 120 mi/h. The pilot sees…

A: Given:

Q: In order to write the weather report for the school newspaper, Jeremiah measured the amount of snow…

A: topic - rate of change  rate of change  is 0.5 inch/hour

Q: The value of a machine, V, at the end of t years is given by v=C(1-r)t, where C is the original cost…

A: Consider the function for machine value: v=C1-rt v=Future valueC=Original costr=Ratet=Time

Q: The temperature in a laboratory is maintained at 20°C. A warm bath is left to cool down and the rate…

A:

Q: Q1. In a study of Bacterial Growth, it is assumed that, a culture initially has Po number of 5…

A: The formula for exponential growth or decay is given by the expression: At = A0ekt Here, A(t) is…

Q: The value of a machine, V, at the end of t years is given by V=C(1-r)t, where C is the original cost…

A: Solution -  Value of the machine = V Time in years = t Original cost of the machine = C Rate of…

Q: Media consultants for the new local magazine IT-Solutions! have projected that the number of sub-…

A:

Q: Two trains travel from New Orleans to Memphis in 4 h. The first train travels at a constant velocity…

A: We have given that two trains travel from New Orleans to Memphis in 4h .The first train travels at a…

Q: Given a function f(x)=e2x−ex+1, what is the correct form of the relative rate of change R?

A: Given: The function is given by f(x)=e2x-ex+1   To determine:  The correct form of the relative rate…

Q: When a factory operates from 6 AM to 6 PM, its total fuel consumption varies according to the…

A:

Q: The height of a tree is approximated by h(t) = 48/ 1 + 240^e−0.2t where t is the age of the tree in…

A: Given,h(t)=481+240e-0.2there,h(t)=24…

Q: The velocity of a plane (km/h) flying into an increasing headwind is v=50(12−t), where t is the time…

A:

Q: The value of a machine, V, at the end of t years is given by V=C(1-r)t where C is the original cost…

A: Given,          The value of a machine, V, at the end of t years is given by V=C(1-r)t ;…

Q: An ice cube has a side length of 5 cm. The ice cube is melting, and the formula is given as V = (5 –…

A: The average rate of change of a function f(x) from to is defined by . The instantaneous rate of…

Q: A car is driving away from a crosswalk. The formula d=t2+3t expresses the car's distance from the…

A:

Q: When the Covid-19 vaccine is injected into a muscle, the muscle responds by contracting. The amount…

A: our objective is to find the concentration.

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

A: As per given by the question, the patient's temperature is given by; . Now, First finding the…

Q: dP The rate of pressure increase that a particular diver feels as they desend is given by = 3y2 +…

A: dPdy=3y2+12y+7⇒dP=3y2+12y+7 dy Now integrating on both sides, we get ∫dP=∫3y2+12y+7…

Q: Ontario's vaccine booking website will be used to schedule covid 19 vaccination appointments for…

A: To solve the following problem

Q: Find the producers' surplus at a price level of p= $57 for the price-supply equation below. p= S(x)…

A:

Q: The DeWitt Company has found that the rate of change of its average cost of producing a product is C…

A:

Q: A is 60 miles from B. An automobile at A starts for B at the rate of 20 milesan hour at the same…

A:

Q: The Reed-Frost model for the spread of an epidemic predicts that the number I of newly infected…

A:

Q: D. Now that you know the equation of the line of best fit, use the equation to estimate the BMI of a…

A: Use EXCEL to determine the regression equation.   EXCEL procedure:   Go to EXCEL Go to Data>Data…

Q: Two autos, P and Q, start from the same point and race along a straight road for 10 seconds. The…

A: Given, velocity of auto P is given by a) First to find the time t when actual acceleration and…

Q: he radius of a circle is increasing at a rate of 2 ft/min. At what rate is its area changing when…

A: Area of the circle , A =πr2, where 'r' is the radius of the circle.

Q: The value of a machine, V, at the end of t years is given by V = C(1 – r)', where Cis the original…

A: The value of the machine is:-

Q: At the beginning of a snowstorm, Harper had 11 inches of snow on her lawn. The snow then began to…

A:

Q: dE The rate at which a machine operator's efficiency, E (expressed as a percentage), changes with…

A: To find thw operator's efficiency, we need to find the the differential equation.

Q: Find the rate of change of total revenue, cost, and profit with respect to time. Assume that R(x)…

A:

Q: Two trains travel from New Orleans to Memphis in 4 h. The first train travels at a constant velocity…

A: Velocity is the rate of change of the position of an object w.r.t a frame of reference as a function…

Q: At time t=U years, a ranch has a population of 25 deer If the rate of growth of the population is…

A:

Q: dC The rate of change in the concentration of a drug with respect to time in a user's blood is given…

A:

Q: ,A large cube of ice melts such that it maintains its shape. The surface area is decreasing at the…

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.