Consider the function price = $100 – ($3/yr) x time. The initial value of this function is

Q: 3. A rocket weighs 2000 tons at liftoff and burns fuel at a rate of 10 tons/minute. Express the…

A: Given query is to find function of the weight after t time of the liftoff.

Q: The price P (in dollars) of a used car is a function of its initial cost C (in dollars) and its age…

A: P is the price of a used car and A is the age, the unit of P is in dollar and that of A is year.

Q: The monthly profit, P(x), of a company is expectedyto change at the rate of 6,498 P' (x) = 3 – (2т -…

A:

Q: The annual sales for a fast food restaurant are $650,000 and are increasing at a rate of 4% per…

A: Given, Annual sales for restaurant= $650,000 Rate=4%   Exponential growth function (Y) Let 'P' be…

Q: A 500 gallon oil spill undergoes a cleanup process. The company hired to clean the spill can remove…

A: It is given that 15% of the spilled oil gets cleaned and initially there are 500 gallon of oil is…

Q: A stone is dropped into a lake, creating a circular ripple that  travels outward at a speed of 60…

A: We have given the speed of the circular ripple is v=60 cm/s. That means the radius of circular…

Q: Construct a function for the following scenario. The total cost of renting a vacation home includes…

A: The equation of the line can be represented as y = mx + c, where c is a constant and m is the slope.…

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

A: Let the distance be measured from the surface of ocean. The distance be represented by variable h…

Q: certain cellphone company offers a plan that costs P1,200.00 er month. The plan includes 180 free…

A: Given that

Q: 3. A bucket that weighs 3 lb and a rope of negligible weight are used to draw water from a well…

A:

Q: d (x+;

A: Here we use chain rule of differenciation.

Q: The resale value V of a piece of industrial equipment has been found to behave according to the…

A: given function V=150,000e-0.075t (a) what was the original value of the piece of equipment? put t=0…

Q: A jogger ran 4 miles and then walked 2 miles. The average velocity running was 3 miles per hour…

A: Given  A jogger ran 4 miles and then walked 2 miles. Total time is T  The average velocity of…

Q: The function I (t) = - 0.2t3 + 3t2 +100  for 0 ≤ t ≤ 9 gives the CPI of an economy, where t = 0…

A:

Q: The rate of natural increase of the population of a certain city is proportional to the population.…

A:

Q: (***) The concentration of a certain drug, in mg/L, can be modeled by the following function: C(t)=…

A: Given function is,

Q: The monthly profit, P(x), of a company is expected to change at the rate of 6,498 P' (x) = 3 (2а —…

A: THE SOLUTION IS GIVEN BELOW

Q: An object dropped from a height of 400 feet has a height, h(t), in feet after t seconds have…

A: Given : h(t)=400-16t2   To find : a) t(h)b) time to reach height of 350 feet

Q: The function P =f(n) = 45127(0. 943)“ models the anticipated population, P, of a small town in…

A: Given, P=fn = 451270.943n  Where P is the population of the town and n represent the number of years…

Q: A rocket sled having an initial speed of 139 mi/h is slowed by a channel of water. Assume that…

A:

Q: The rate (in mg carbon/m /h) at which photosynthesis takes place for a species of phytoplankton is…

A:

Q: Find the total income produced by a continuous income stream in the first 5 years if the rate of…

A:

Q: In the feasibility test for the flight movement of a drone, it is known to have a function of the…

A:

Q: Using the initial value and elimination rate, write a function that can be used to model the amount…

A: here initial value is 0.19 so the y-intercept is  c=0.19 . and the command difference between the…

Q: c. Use function notation to represent the change in Sam's height above the ground over the time…

A: (c) The function notation to determine the change in the "S" height from t=4 to t=10 seconds is,…

Q: Between 1990 and 2000, Nevada was the fastest growing state in the nation, with an annual growth…

A:

Q: The function y = f(x) is graphed below. What is the average rate of change of the function f (x) on…

A: Average rate of change of function f(x) in the interval [a, b] is as follows. Ax=fb-fab-a

Q: Find the average rate of change of the function f(x) 2-2x + 4, from x = -4 to x = 2. Average rate of…

A: Given : fx = x2-2x+4x

Q: MAR 17. An elementary school is having sand delivered for the pla charges $5.00 per ton of sand plus…

A: In this question, graph of function is obtained. Graph of Function The graph of a function is the…

Q: The function given below gives the cost to manufacture x items. Estimate (using h = 0.0001, the…

A: We have to find C'(120)  We will use the limit definition of the derivative. For that we have to…

Q: A cup of coffee has a temperature of 200° ? and is palced in a room that has a temperature of 70° ?.…

A:

Q: Divers in Acapulco, Mexico, dive headfirst at 8 feet per second from the top of a cliff 87 feet…

A: Use the position function s(t) = −16t2 +v0t + s0Where,v0 = initial velocitys0 = initial positiont =…

Q: Use the given graph to estimate the value of each derivative.  (a) f ′(−3) (b) f ′(−2) (c) f ′(−1)…

A:

Q: A stone is dropped into a lake, creating a circular ripple thattravels outward at a speed of 60…

A: (a) Express the radius of this circle as a function of thetime t(in seconds).

Q: Differentiate and simplify this function:  e√t^2+t+1 - e-√t^2+t+1

A:

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: A bacteria colony grow at a rate of 11% per year. If the initial sample has a mass of 500 grams,…

A: Solution:- function is missing in the question , but according to formula i have solved the…

Q: Rewrite the function in the form y= a(1+ r)t or y= a(1- r)t. Then state the growth or decay rate. y=…

A:

Q: A startup business projects its instantaneous rate of revenue flow to be given by R(x)=120,000e^.03t…

A:

Q: 3. The height of a rocket, h, is increasing at a rate of 18 feet per second. If its height at five…

A: The height of a rocket, h, is increasing at a rate of 18 feet per second. If its height at five…

Q: If a bullet from a pistol is fired straight up from the ground, its height t seconds after it is…

A: the bullet from a pistol is fired straight up from the ground, its height t seconds after it is…

Q: If a baseball is projected upward from ground level with an initial velocity of 32 feet per second,…

A: SINCE YOU HAVE ASKED MULTI PAL QUESTIONS IN SINGLE REQUEST , WE WILL BE ANSWERING ONLY THE FIRST…

Q: The monthly profit, P(x), of a company is expected to change at the rate of 6,498 P'(x) = 3 – (2а —…

A:

Q: The following functions give the total cost of owning different cars as a function of the number of…

A:

Q: (a) Find the final value of f(t) using the final value property. (b) If the final value is not…

A: Given that Laplace Transform of f(t) is  F(s)=10s+1s2+2 We can write it as…

Q: Consumers buy x watches at $p by function x=(5000)/(0.2p+1). Find demand and instantaneous rate of…

A:

Q: The figure shows a page with 1-inch margins at the top and the bottom and half-inch side margins. A…

A: Let the length and width of the printed page be y and x, respectively. Given printed area of page is…

Q: A football player kicks a ball at an angle of 37° above the ground with an initial speed of 20…

A: h=0.75d-0.0192d2 Solution is in next step and final answers are in last step

Q: The average weight, W, in pounds of an adult is a function, W=f(c), of the average number of…

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.