a company bought the k machine for 2.000 $ The value of the machine decreases over time depending on the f(t) = P 0e-0,07t function. When will the value of the machine be 20 $ ? Please explain whether the value of the machine is 0 mathematically according to this model.

a company bought the k machine for 2.000 $ The value of the machine decreases over time depending on the f(t) = P 0e-0,07t function. When will the value of the machine be 20 $ ? Please explain whether the value of the machine is 0 mathematically according to this model.

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.2: Domain And Range

Problem 60SE: The height h of a projectile is a function of the time t it is in die air. The height in feet for t...

See similar textbooks

Related questions

Q: If an archer shoots an arrow straight upward with an initial velocity of 160ft/sec from a height of…

A: If the arrow reaches the ground then h(t)=0…

Q: The temperature in degrees Celsius (C) in Toronto starting on March 1** can be represented by the…

Q: The rate of change in the number of urban transit vehicles such as buses and light-rail trains, in…

Q: The function f(x) = 4ᴫx3/3 describes the volume, f(x), of a sphere of radius x inches. If the radius…

A: f(x) = 4πx33 Volume of sphere , f(x) = 4πx33 where, x is the radius of sphere in inches.…

Q: Between 2006 and 2016, the number of applications for patents, N, grew by about 3.2% per year. That…

Q: The function f(x) = (4/3) πx3 describes the volume, f(x), of a sphere of radius x inches. If the…

A: fx=43πx3 Differentiating with respect to x, we get f'x=ddx43πx3=43π·3x2 ∵dxndx=nxn-1=4πx2

Q: Between 2006 and 2016, the number of applications for patents, N, grew by about 4.3% per year.…

A: To solve the following problem

Q: Q5 Find the instantaneous rate of change at 2 for: f(x) = 6x2-9x -6

A: The given function is,

Q: Juanita wishes to have a rectangular garden in her backyard with an area of 64 ft2. Letting x denote…

A: we know that area of rectangle = length × width

Q: The function f(x) = x3 describes the volume of a cube, f(x), in cubic inches, whose length, width,…

A: Given volume function fx=x3 to find instantaneous rate of change of the volume x=4 in

Q: Find f" (1) when f(x) = x² − 3x³ + 2x² +10. Round your answer to three decimal places, if necessary.

Q: The revenue (in dollars) from the sale of x car seats for infants is given by the following…

Q: An accessories company finds that the cost, in dollars, of producing x belts is given by C(x) = 780…

A: Given : Cost function : C ( x ) = 780 + 35 x - 0.063x2 Find the rate at which average cost is…

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

Q: The revenue (in dollars) from the sale of x car seats for infants is given by the following…

A: The given function for the revenue from sale of x no. of car seats for infants is R(x)=28x-0.010x2…

Q: A 2,916-liter cistern is empty when water begins flowing into it (at t=0) at a rate (in L/min) given…

Q: the temperature of a pot of coffee after brewing can be determined by the function…

A: Given temperature function is: F(t)=104e-0.0245t+76

Q: The number of applications for patents, N. grew dramatically in recent years, with growth averaging…

Q: Between 2006 and 2016, the number of applications for patents, N, grew by about 4.9% per year. That…

A: Given: N'(t)=0.049 N(t)Therefore:dNdt=0.049 N

Q: In 2003 the number of online viewers was projected to grow according to the function. N(t)= 52t0.531…

A: As t=1 corresponds to 2003 then the value of t corresponds to 2010 is 2010-2003+1=8 Put this t=8…

Q: As a → 1 what happens to the value of f f(x)dx?

A: As a →1 what happens to the value of ∫1af(x)dx.

Q: Find the average rate of change of f(x) = 9x² – 3 on the interval [2, t]. Your answer will be an…

A: Use formula of avg rate of change

Q: 3. Armaan claims that the functions f(x) = 32x + 5 and g(x) = 32* + 8 have different instantaneous…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: What is the equation of the function that is obtained from f (x) = | x | by reflecting about the x…

A: Given information:The given function is

Q: The function f(æ) can be approximated by L(x) = 3 – 2(x – 4), near x = 4. What is the value of f'…

A: topic -linear approximation

Q: 5. Consider the population of bacteria grows according to the function f(t) 200e0.02t, where t is…

A: The solution of the problem is given in the next steps.

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

A: Given problem:- Find the point of diminishing returns (x,y) for the function R(x), where R(x)…

Q: Between 2006 and 2016, the number of applications for patents, N, grew by about 4.8% per year. That…

A: given: Between 2006 and 2016, the number of applications for patents N, grew by about 4.8 % per…

Q: Between 2006 and 2016, the number of applications for patents, N, grew by about 4.1% per year. That…

A: (a) N'(t)=0.041N(t)dNdt=0.041NdNN=0.041dt∫dNN=∫0.041dtln N=0.041t+celn…

Q: y = Va+1-3

Q: An accessories company finds that the cost, in dollars, of producing x belts is given by C(x) = 720…

Q: Find the average rate of change of f(x) = 7x² – 4 on the interval (3, b]. Your answer will be an…

A: Finding the average rate of a function in a given interval

Q: The surface area of a hot-air balloon is given by the function S(r) 4Tr", where r is the radius of…

A: NOTE: Refresh your page if you can't see any equations. . the radius is increasing at a rate of…

Q: It is estimated that a worker in a shop that makes picture frames can paint y frames t hours after…

A: The given function is: y=3t-8t2-t3, 0≤t≤4 where y is the number of frames painted in t hours. Here,…

Q: In the manufacture of printing ink, solvents are used to suspend or dissolve the pigments that give…

A: Rt=10t5t2+4

Q: The number of bacteria in a culture is modeled by the function n(t)=30e^rt where t is in hours.…

Q: Find the average rate of change of f(x) = 9x2 – 8 on the interval [2, t]. Your answer will be an…

Q: The revenue (in dollars) from the sale of x car seats for infants is given by the following…

A: R(x)=24x-0.010x20≤x≤2400 To find average change in revenue apply formula…

Q: A 8,000-liter cistern is empty when water begins flowing into it (at t= 0) at a rate (in L/min)…

A: Given the function for rate of water flowing is, Here t is measured in minutes. a. Given the time…

Q: A 12,000-liter cistern is empty when water begins flowing into it (at t = 0) at a rate (in L/min)…

A: Note: As per the guidelines we are supposed to answer only 3 sub parts, kindly repost the complete…

Q: There is a bacteria cell in a Petri dish that is reproducing at a rate of r(t) = 2t^2+1…

A: Solution:

Q: A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function…

A: A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by

Q: The function f(x) = 4ᴫx2 describes the surface area, f(x), of a sphere of radius x inches. If the…

A: Given: The surface area of a sphere is, fx=4πx2 . Radius of the sphere is, x=6 inches. The…

Q: The rate A (in tons per year) at which a pollutant is being dumped near a city is given by the…

Q: A 7,986-liter cistern is empty when water begins flowing into it (at t= 0) at a rate (in L/min)…

Q: Use the position function below to solve the following problem. A projectile is fired vertically…

Q: Find the average rate of change of f(x) = 7x² – 4 on the interval [3, b]. Your answer will be an…

Q: Find the average rate of change of f(x)=9x2−8 on the interval [4,b]. Your answer will be an…

A: Given function , f(x)=9x2-8 on the interval 4,bThe average rate of change of fx=9x2-8 is in…

Q: The function y is discontinuous at x equals? x+2

A: Given function is: y=x-4x+2

Concept explainers

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.

Question

a company bought the k machine for 2.000 $ The value of the machine decreases over time depending on the f(t) = P ₀e^-0,07tfunction. When will the value of the machine be 20 $ ? Please explain whether the value of the machine is 0 mathematically according to this model.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differential Equation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

What is the composition of two functions, fg ?
Use your schools library, the Internet, or some other reference source to find real-life applications of approximations of functions.
When a certain drug is taken orally, the concentration of the drug in the patient's bloodstream After t minutes is given by C(t)=0.06t0.0002t2 where 0t240 and concentration is measured in mg/L .When is the maximum serum concentration reached, and what is that maximum concentration?
Repeat the previous exercise to find the formula forthe APY of an account that compounds daily. Usethe results from this and the previous exercise todevelop a function I(n)for the APY of any accountthat compounds n times per year.
For the following exercises, consider this scenario: A town has an initial population of 75,000. It grows at a constant rate of 2,500 per year for 5 years. Find a reasonable domain and range for the function P.
The radius r, in inches, of a spherical balloon isrelated to the volume, V, by r(V)=3V43 . Air is pumped into the balloon, so the volume after t seconds is given by V(t)=10+20t . a. Find the composite function r(V(t)) . b.Find the exact time when the radius reaches 10 inches.
The height h of a projectile is a function of the time t it is in die air. The height in feet for t seconds is given by the function h(t)=-16t2+96t . What is the domain of die function? What does the domain mean in the context of die problem?
For the following exercises, consider this scenario: The number of people afflicted with the common cold in the winter months steadily decreased by 205 each year from 2.005 until 2010. In 2005, 12,025 people were afflicted. Find the linear function that models the number of people in?icted with the common cold, C, as a function of the year, t.
The cost in dollars of making x items is given by the function Cx)=10x+500. a. The fixed cost is determined when zero items are produced. Find the fixed cost for this item. b.What is the cost of making 25 items? c.Suppose the maximum cost allowed is SI500. What are the domain and range of the cost function, C(x) ?