9. The rate at which the value, V, of a painting changest years after it is completed is given by the function RV(t). 2 6t + 4t + 10 (in dollars/year), what is the net change in the value of the (a) If RV(t) painting from 1 year after it's completed to 4 years after it's completed? (b) If RV(t) = \6t + 2 (in dollars/year), give a lower estimate for the net change in the value of the painting from 1 year after it's completed to 3 years after it's completed using a Riemann sum with 6 rectangles.

Q: 3. A manufacturer determines that when x thousand units of a particular commodity are produced, the…

A: Given that: Profit function: P(x)=-400x2+6800x-12000

Q: The volume of fluid in an IV (intravenous) drop decreases according to the mathematical model…

A: The  given model of the volume of fluid in IV drop versus time is:   V=-0.110t+1   Where, V is the…

Q: 13. a) Determine the average rate of change over the interval x = [1, 5] of the function y = 3x + 1.…

A: To solve the following

Q: Suppose that a company can produce 12,000 units when the number of hours of skilled labor y and…

A:

Q: For a short run production function q=10lnL if L=5 and the wage rate is $3 the extra cost of to…

A: Answer:----.               Date:----3/10/2021

Q: a. Suppose that Miller Corporation can produce 3500 refrigerators when the number of hours of…

A:

Q: 2. Malik, the business manager of a company that produces in-ground outdoor spas determines that the…

A:

Q: When a certain product is sold for p dollars per item, consumers will demand D(p)= 12,00p^-1 items…

A: Given, D(p)= 1200p-1 items/week p(t)= 0.5t²+6 dollars/item

Q: Suppose a company wants to introduce a new machine that will produce a rate of annual savings​ (in…

A: given S'x=150-x2C'x=x2+114x where S'x is the rate of annual saving and C'x is the rate of annual…

Q: Suppose you are climbing a hill whose shape is given by the equation z = 1000 −0.005x^2 −0.01y^2…

A:

Q: The economic dependency ratio is defined as the number of persons in the total population who are…

A: We need to find the value of x for which R(x) has minimum. Here, R(x)=-0.0002x3+0.052x2-4.06x+192.…

Q: 2. Suppose that the marginal revenue for a company manufacturing coffee machines is given by…

A: Given expression for marginal revenue of the company is: Q=100-0.5x where, Q is the marginal revenue…

Q: An article† in The New York Times states, "The number of gas stations [in a city] grows only in…

A: Part (a):To compare the number of gas station.

Q: When they invest K dollars, a fishery can produce Q(K) pounds of fish per month, where Q(K) = 104…

A: Rate of change is nothing but the change happen in any observations over a period of time. Here…

Q: 2. What is the average rate of change between x = 2 and x = 3 for the function g(x) = 5(x – 2) - 3 ?

A:

Q: Suppose that the cost of producing x items is C(x) = .005x3 - .5x2 + 28x + 300 dollars, and daily…

A: Cx=0.005x3-0.5x2+28x+300 a). The extra cost of increasing daily production from 50 to 51 items is,…

Q: 3. Imagine you fill your bathtub up at a rate of 2 gallons per minute. This means that every minute…

A:

Q: 8. Create the equation of any function where the instantaneous rate of change when x = 1 does not…

A: Create the equation of any function where the instantaneous rate of change when x = 1 does not…

Q: Suppose that the total profit in hundreds of dollars from selling x items is given by…

A:

Q: Suppose that the intensity of a point light source is directly proportional to the strength of the…

A:

Q: A company finds that the rate at which the quantity of a product that consumers demand changes with…

A:

Q: The economic dependency ratio is defined as the number of persons in the total population who are…

A: To find the year in which the economic dependency ratio reached its minimum

Q: suppose that the price p(in dollars) and the weekly sales x (in thousands of dollars) of a certain…

A: Given query is to find rate of change of sales.

Q: 3. Suppose that for a company producing r face shields per week, the cost (C) and revenue (R)…

A:

Q: 4. Suppose that the marginal propensity to consume is dc 0.7-ey (in billions of dollars) dy and that…

A:

Q: The number of U.S. citizens aged 65 years and older from 1900 through 2050 is estimated to be…

A:

Q: An articlet in The New York Times states, "The number of gas stations [in a city] grows only in…

A: We will use the given relation between population and gas station.

Q: Suppose that the marginal propensity to consume is   dC dy = 0.02 +  ln(y + 1) y + 1      (in…

A:

Q: Suppose that the revenue (in dollars) from the sale of a product is given by R = 30x + 0.8x2 −…

A:

Q: Suppose that the monthly cost, in dollars, of producing x chairs is C(x) = 0.001x° +0.07x + 14x +…

A:

Q: Suppose that the daily profit (in dollars) from the production and sale of x units of a product is…

A: x is the number of units produced and sold. The Profit function is given by P = 150x − x^2/500−…

Q: Suppose that value of wine respect to time is given following function V = 100e ve. How long will it…

A:

Q: 13. The revenue from a manufacturing process (in millions of dollars) is projected to follow the…

A: R = 100 + 0.08t at t = 10 R = 100 + 0.8 R = 100.8 million dollars.   C = 60 + 0.2 t2 at t = 10 C =…

Q: An article† in The New York Times states, "The number of gas stations [in a city] grows only in…

A: Let N be the population in millions and G be the number of gas stations in a city. Given that the…

Q: One method of slowing the growth of an insect populationwithout using pesticides is to introduce…

A: Given as: Females grows at a rate of  r = 0.10 Number of males S=900 Then:…

Q: An article† in The New York Times states, "The number of gas stations [in a city] grows only in…

A: It is give that population is N and G be the number of gas stations in a city related by G=cN0.77.…

Q: Suppose that the daily profit (in dollars) from the production and sale of x units of a product is…

A:

Q: Suppose that the yield (measured in kg/ ha) of an agricultural crop is represented by the function…

A: We need to find rate.

Q: 2. A property agent handles an office building with 50 identical offices for rental. Experience…

A: 50 offices occupied corresponding to $800 49 offices corresponding to $820 Plot the two points and…

Q: Suppose a company has fixed costs of $12,300 and variable cost per unit of $0.20 x+128 dollars,…

A:

Q: Suppose total cost in dollars from the production of x printers is given by C(x) = 0.0001x3 +…

A:

Q: What is the instantaneous rate of change at x = 2 of the function f given by 2x f(x) O O 4 -2 H N -…

A: What is instantaneous rate of change at x=2 of the function f given by   f(x)= 2x/x-1

Q: Suppose that the profit (in dollars) from the sale of Kisses and Kreams is given by P(x, y) = 10x +…

A: Px,y=10x+6.2y-0.008x2-0.02y2

Q: Suppose that the marginal propensity to save is ds = 0.95 - dy In(y + 1) (in billions of dollars) y…

A: According to question given :dSdy=0.95-lny+1y+1Consumption is $6.03 when disposable income is $0

Q: 10. Find the equation of the curve whose slope is the inverse of the sum of the square root of five…

A: Given ,  We have to find the equation of the curve whose slope is the inverse of the sum of the…

Q: An articlet in The New York Times states, "The number of gas stations [in a city] grows only in…

A: given that G=cN0.77

Q: Suppose that a company can produce 12,000 units when the number of hours of skilled labor y and…

A:

Q: 2. The instantaneous rate of change of g(x) is the same for every real value of x. What conclusion…

A:

Q: Suppose the average daily metabolic rate for certain types of animals can be expressed as a function…

A:

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.