s(t) = 10,000 + 10,000 cost Sales of snow shovels are seasonal. Suppose the sale of snow shovels (in dollars) in Maine is approximated by is time in months and t = 0 is October. What are the sales in December? where t a $13,900 $17,071 Oc $18,660 O d $15,000

Q: The daily cost C (in dollars) for a manufacturer to produce z electronic video components is given…

A: given cost function is c(x) = 1000 . ln((2x^2-700)^1/3) here we have to calculate the change of cost…

Q: On a college campus of 5,000 students, one student returns from vacation with a contagious flu…

A: Given:

Q: S(r) = 3x2 – 5x+ 10 What is the rate of change as x goes from r=2 to r =3?

A: Given data :  f(x) = 3x2 - 5x + 10 x1 = 2 to x2 = 3

Q: Consider the following. = -0.1s3 + 6s² + 400 Find the amount s of advertising (in thousands of…

A: The point of diminishing returns refers to the inflection point of a return function or the maximum…

Q: ne de Medici wants to purchase sc es at a price of 10 livre tournois. rice that she would purchase…

A: given initial quantity =5.5 tonnes intial price = 10 livre tournois according to question for…

Q: Your automobile assembly plant has a Cobb-Douglas production function given by q = x0.4,0.6 where q…

A:

Q: On a college campus of 3000 students, the spread of flu virus through the student is modeled by…

A: The logistic growth rate model always produces an exponential function. If the model contains the…

Q: The surface area S (in square meters) of a hot-air balloon is given by S(r) = 4xr where r is the…

A: If f is a function of x and x is a function of t, then ft is nothing but the composite function fxt.…

Q: Suppose that the distance an aircraft travelsalong a runway before takeo’ is given by D = (10/9)t2,…

A:

Q: Your automobile assembly plant has a Cobb-Douglas production function given by q = x0.4y0.6 where q…

A:

Q: Your automobile assembly plant has a Cobb-Douglas production function given by q = x0.4y0.6…

A: Annual operating costs amount to an average of $20,000 per employee plus the operating budget of…

Q: d*y 4. Find 5 of the function f (x) = - e dz"

A:

Q: If an object is dropped from a 192-foot-high building, its position (in feet above the ground) is…

A: Given data:   The height of the building is h=192 feet. The given expression for the position of the…

Q: The revenue R of skiing facilities in the united states from 2000 through 2008 can be modeled by…

A: Given, R=1548e0.0617t So, the rate of change of revenue with respect to time dR/dt =  1548 *…

Q: Suppose the demand for a certain item is given by D(p)=-2p2-5p+900, where p represents the price of…

A:

Q: The position of a moving object is S(t) =t-3t-9t-1 meters to the right of 0 in t seconds. (a) When…

A: Explanation: Given that,  Position of a moving object is defined as,                             a)…

Q: A population of bacteria is growing according to the equation P(t) = 650e".22. Estimate when the…

A:

Q: The cost of a personal computer is $700 and its value is depreciating with time according to the…

A:

Q: An employment research company estimates that the value of a recent MBA graduate to an accounting…

A:

Q: An environmental protection agency discovered in the beginning of 2009 that a waste dump has been…

A: Let's find

Q: The percentage of P doctors who accept a new medicine is given by P(t)=100(1-e^-0.16t) Where t=time…

A:

Q: The time, t, in weeks, needed for the population of fireflies in a field to reach p individuals is…

A: t(p)=45ln[10,000/(18,000-p)] We have to find the population, p when t = 5

Q: The number of books in a small library increases according to the function B= 3700e0.05t, where t is…

A: Given,The number of books in a small library increases according to the function B= 3700e0.05t,…

Q: The position of an airborne object at any time t is given by h(t) = -9.8t2 + 25t + 10. At which…

A: Consider the position of airborne object is given by function: ht=-9.8t2+25t+10 Find the values of t…

Q: A certain bakery has found that the daily demand for bran muffins is 17500/p where p is the price of…

A: Equate the demand and supply equation to get the price P

Q: Suppose that the distance an aircraft travels along a runway before takeoff is given by D =…

A:

Q: Suppose that SpaceX launches a rocket at t = 0 seconds and that its height, in meters above…

A:

Q: If an object is dropped from a 150-foot-high building, its position (in feet above the ground) is…

A: Negative sign of the velocity is due to the downward movement of the body.

Q: The cost function for a weekly manufacture of headphones is given by C(2) = 150, 000 + 20r + 0.012…

A: solution:-

Q: Farmer Lindsey estimates that after t days, her crop will be increasing at a rate of r(t)  =  15t8 +…

A: Solution ) r (t) = 15t8 + e-0.76t when t = 0 r(0) = 15×(0)8 + e--0.76×0 r(0) = 0 + e0 r(0) = 0 + 1…

Q: Q7) A company sells a product for $150 per unit. Raw material costs are $40 per unit, labor costs…

A:

Q: The height of a ball after being dropped from a point 100 feet above the ground is given by h = −16t…

A: When the ball is 60 feet above the ground, then h=60. When the ball hits the ground, then h=0.

Q: Find the point of diminishing returns (x.y) for the function R(x), where R(x) represents revenue (in…

A:

Q: An ice cream shop estimates that the revenue (in dollars) from the sale of x cones is given by R(x)=…

A: Given: - The revenue from the sale of x cones is given byR(x)=11000ln0.02x+1 To find: - The change…

Q: A bottle manufacturer has determined that the cost (C) in dollars of producing xr bottles is C =…

A:

Q: The surface area S (in square meters) of a hot-air balloon is given by S(r) = 4tr where r is the…

A: find the surface area S of the balloon as a function of the time t.

Q: A population of bacteria is growing according to the equation P(t)=1700e0.17t. Estimate when the…

A:

Q: Suppose that the distance an aircraft travels along a runway before takeoff is given by D= (5/3)r,…

A: Given that: D=53t2

Q: The value of China's exports of automobiles and parts (in billions of dollars) is approximately f(z)…

A: Substitute f(x)=6.8 in the equation of f(x) and solve for x to find its value. Use the value of x to…

Q: Suppose that a vending machine service company models its income by assuming that money flows…

A: *to find:- total income over the first 3 years. *concept:- integration of e^{ax} = (e^{ax})/a.

Q: A car driving along a freeway with traffic has travelled s(t) =r' – 31* + 3t + 20 meters in t…

A:

Q: The monthly demand for insulated coffee mugs is given by q= 4400 − 200p, where p is the price of a…

A:

Q: Suppose it has been determined that the sales at the gallery decline after the end of advertising…

A: Consider the model function for daily sales after the end of advertising campaign is S=7000-2-0.1x,…

Q: A minute ad during a campaign in 1973 cost $200,000. The price tag for a 30-second ad slot during a…

A: We are given that the cost of 30-second slot of advertising for a campaign can be modeled by…

Q: Demand for an electric fan is related to its selling price p (in dollars) by the equation n = 1960 –…

A: n=1960-70pn= number of fansp = price

Q: A shoe company is planning a new brand of walking shoe for the market. Research shows that x, the…

A: A function f(x) is said to be differentiable at x=a where a∈m, n,if: limh→0fa+h-fah A function f is…

Q: If an object is dropped from 182 foot high building, it's position (in feet above ground) is given…

A: Given that, an object is dropped from 182 foot high building. It’s position is given by,

Q: A population of bacteria is growing according to the equation P(t) = 1950eº population will exceed…

A:

Q: tổ approximate the change in profit corresponding to an increase in sales (or production) of one…

A: Given that: P=-0.1x3+400x-60, x=50and dx=∆x=1

Q: the average price of a two-bedroom apartment in downtown New York City during the real estate boom…

A: Given average prize : p(t) = 0.33e0.16t million dollars  t=0 represent 1994 in 1995 i.e…

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.