The average cost of a product changes at the rate C '(x) = -20/x2 + 1/10 and the average cost of 10 units is $20.00. (a) Find the average cost function. C = (b) Find the average cost of 70 units. (Round your answer to two decimal places.)

The average cost of a product changes at the rate C '(x) = -20/x2 + 1/10 and the average cost of 10 units is $20.00. (a) Find the average cost function. C = (b) Find the average cost of 70 units. (Round your answer to two decimal places.)

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Polynomial Functions

Section3.5: Mathematical Modeling And Variation

Problem 6ECP: The resistance of a copper wire carrying an electrical current is directly proportional to its...

See similar textbooks

Related questions

Q: Suppose the cost function of a product is given as C=3q -0.0014³. If the cost is increasing at a…

Q: he marginal cost (rate of change of cost) in euros per unit of production for artilugios in a ertain…

Q: One hundred strands of bacteria are placed in a nutrient solution in which a plentiful supply of…

Q: The cost of producing x units of a certain commodity is c(x) = 1000 +5.70x +.7x2. What is the…

Q: 2. The total cost, C (in thousand of dollars), of producing x (in hundred) units of some commodity…

Q: A fluid is being pumped from a cylinder into a rectangular prism with a square base. The base has…

Q: A bacteria culture starts with 1000 bacteria, and after 2 hours the population is 2500 bacteria.…

Q: The length x of a rectangle is decreasing at a rate of 5cm/seconds and the width y increasing at a…

Q: a tank initialy holds 80 gallon of a brine solution containing 1/8 lb of salt per gallon. at t=0,…

Q: Initially 50 grams of radioactive substance was present. After 6 hours the mass had decreased by 9%.…

Q: As part of the process in the production of a perfume, a certain substance with water is converted…

A: We will find the amount conveted in the given time.

Q: = Find out (i) P/V ratio, (ii) Fixed Cost (iii) Sales volume to earn a Profit of 745,000. From

Q: Suppose the total cost (in dollars) for a product is given by `C(x)=200x+20\ln(x)` where `x` is the…

Q: 2. The number of bacteria at the beginning of an experiment was 30 and the bacteria grow at an…

A: Given The number of bacteria at the beginning of an experiment = 30 hourly growth rate = 1.4%

Q: a tank initialy holds 80 gal. of a brine solution containing 1/8 lb of salt per gallon. at t=0,…

Q: Initially a tank contains 10 lb of salt dissolved in 100 gal of water. Assume that brine containing…

A: Given that Initially a tank contains 10 lb of salt dissolved in 100 gal of water. Let x(t) be the…

Q: A tank initially holds 1 cubic meter of a brine solution containing 20 kg of salt. Att= 0, fresh…

Q: 2. An object moves along the graph y = x° – 2x – 17, starting from the point (0, –17) at time t = 0,…

A: Given that dx/dt= 3 m/sec is constant for all x. So at t=1, x=3, because in 1-second x will move 3m…

Q: In monitoring the blood alcohol content of a person, the bloodstream, which is composed of 5L of…

A: We will formed a differential equation and then solve it to get amount of blood

Q: A 100-gallon tank is full of a solution containing 20 pounds of a concentrate. Starting at time t =…

Q: 6. The amount of pain reliever in Tony's bloodstream decreases at a rate that proportional at any…

A: Let amount of pain reliever in Tony's bloodstream be x Given dxdt=-kx

Q: Suppose a brine containing 2 kg of salt per liter runs into a tank initially filled with 500 L of…

A: Set up a differential equation. Let A(t) denote the amount of salt in the tank at a time t. The tank…

Q: 3 The altitude of a triangle is increasing at a rate of 8 cm/s while its area is increasing at the…

Q: A boat travels 100 miles upstream against a 10 mile/hour current. When the boat's velocity is v…

Q: 2. Carbon decays at a rate proportional to the amount present. The percentage lost is 5% in 150…

Q: Water leaks from a cylinder, with axis vertical, through a small orifice in its base at a rate…

Q: 3 of its radius. 4 Mohamad Salah poured orange juices into a cylindrical red tank whose height f the…

A: Topic:- application of derivatives

Q: A tank initially holds 1 cubic meter of a brine solution containing 20 kg of salt. Att = 0, fresh…

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: A bacteria culture starts with 960 bacteria and grows at a rate proportional to its size. After 4…

A: The exponential growth formula is given by: P(t)=P0 ekt...(1) where P0 is initial population, k is a…

Q: The revenue (in dollars) from the sale of x units of a certain product can be described by R(x) =…

A: R(x) = 100x - 0.09x² So, R'(x) = 100 - 0.09(2x) = 100 - 0.18x &, R''(x) = 0 - 0.18 = - 0.18

Q: A constant volume of pizza dough is formed into a cylinder with a relatively small height and large…

Q: A certain radioactive substance has a half-life of 38 hours. The rate of change in the decay is…

A: Given that rate of decay is proportional tp the current amount x.So,dxdt=kx, where k is…

Q: The radius of a cylindrical tube is increasing at a rate of 2 meters per hour, and the height of the…

A: Cylinder is a figure with circular base with a certain height. We can see it as the below diagram.…

Q: Initially, 10 grams of a radioactive substance were found in a sample. It was observed In z that 20%…

Q: A rectangular sheet of metal has a length of 12 cm decreasing at a rate of 0.2 cm/s, and a width of…

Q: One hundred strands of bacteria are placed in a nutrient solution in which a plentiful supply of…

Q: During the first couple weeks of a new flu outbreak, the disease spreads according to the equation…

A: Let's find rate of inflacted population.

Q: A company sells its product at 60 OMR per unit. The fixed cost is 19500 OMR, and the variable cost…

A: Here we have to find the break even point. We know that break even point is the point where total…

Q: A leaky 10-kg bucket is lifted from the ground to a height of 12m at a constant speed with a rope…

Q: Find the rate of bubble volume increasing when the radus is 4cm if its surface area is increasing at…

A: Given: dSdt=4 cm/secdVdt|r=4 cm=?

Q: Water is leaking out of an inverted conical tank at a rate of 9400.0 cubic centimeters per min at…

A: Explanation: Start by ignoring the leakage and determine the rate of inflow required to achieve the…

Q: A shallow reservoir has a one-square-kilometer water surface and an average water depth of 4 meters.…

Q: Initially 87 grams of radioactive substance was present. After 3 hours the mass had decreased by 6%.…

A: We know that the differential equation of the decaydAdt=kAwhere A = amount and k = proportionality…

Q: The cost in pesos of producing x units of a certain commodity is C(x) = 0.05x2 + 10x + 5000. What is…

Q: The rate of conversion of a certain substance is proportional to the square root of the amount m of…

A: We need to find time.

Q: Tank B, a 30-litre tank, initially contains 6 grams of salt in 15 litres of water. At t = 0,…

Q: Find the instantaneous rate of change for the function at the given value. f(x) = x² + 3x at x = 0…

A: We can find the instantaneous rate of change as below

Q: Early one morning it began to snow at a constant rate. At 7 A.M. a snowplow set off to clear a road.…

Q: A tank containing 100 gallons of brine made by dissolving 40 lbs of salt in water. Pure water runs…

A: Pure water in flow rate = 5 galmin

Q: 1. After 2 days, 10 grams of a radioactive substance is present. Three days later, 5 grams is…

Question

The average cost of a product changes at the rate

C '(x) = -20/x² + 1/10

and the average cost of 10 units is $20.00.

(a) Find the average cost function.

C =

(b) Find the average cost of 70 units. (Round your answer to two decimal places.)

Expert Solution

Step 1

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Chain Rule$

Learn more about

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

Similar questions

The half-life of plutonium-244 is 80,000,000 years. Find function gives the amount of carbon-14 remaining as a function of time, measured in years.
The resistance of a copper wire carrying an electrical current is directly proportional to its length and inversely proportional to its cross-sectional area. A copper wire with a diameter of 0.0126inch has a resistance of 64.9ohms per thousand feet. What length of 0.0201-inch-diameter copper wire will produce a resistance of 33.5ohms?
A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the time read exactly 3:40 p.m. At this time, he started pumping gas into the tank. At exactly 3:44, the tank was full and he noticed that he had pumped 10.7 gallons. What is the average rate of flow of the gasoline into the gas tank?
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) ?
In the year 1985, a house was valued at 110,000. Bythe year 2005, the value hadappreciated to 145,000. What was the annual growth rate between 1985 and 2005 ? Assume that the value continued to grow by thesame percentage. What was the value of the house inthe year 2010 ?
The amount of money in an investment is modeled by the function A(t) = 500(1.079)'. The variable A represents the investment balance in dollars, and t the number of years since 2002. (A) In 2002, the balance was $ (B) The amount of money in the investment is Select an answer (C) The annual rate of change in the balance is r = or r = %. (D) In the year 2008 the investment balance will equal Round answer to the nearest penny. Submit Question
The amount of money in an investment is modeled by the function A(t) = 900(1.0238)'. The variable A represents the investment balance in dollars, and t the number of years since 2007. (A) In 2007, the balance was $ (B) The amount of money in the investment is Select an answer (C) The annual rate of change in the balance is or r = %. r = (D) In the year 2014 the investment balance will equal $ Round answer to the nearest penny.
The value, v of a computer is modeled by the function V(t)=500(0.82)^t where t is the number of years since the computer was purchased. To the nearest tenth of a percent, what is the monthly rate of depreciation?
The value of a car decreases each year. The rate at which the value decreases is called depreciation and is a represented by a percentage. For Alina buys a car for $25,000, and the depreciation rate is 25%. That means that her car’s value goes down by 25% each year. The value can be represented by the function V(y)=25000(0.75)^v, where V represents the value of her car and y represents the number of years that she owns a car. Find the depreciated value of her car if she keeps it for 5 years. In other words, evaluate: V(5)=25000(0.75)^5, rounding to the proper decimal place for money.
A study of driving costs of 2015 model sedan cars found that the average cost (car payments, gas, insurance, upkeep, and depreciation), measured in cents/mile, is approximated by AC(x) = 45+ 120 where denotes the number of miles (in thousands of miles) the car is driven in a X x year. 1. What is the average cost of driving a sedan car 20,000 mi/yr? 2. What happens to the average cost as the number of miles driven increases without bound?
A computer purchased for $1,300 loses 10% of its value every year. The computer's value can be modeled by the function v(t)=a⋅b^t, where v is the dollar value and tt the number of years since purchase.(A) Give the function that models the decrease in value of the computer: v(t)=(B) In how many years will the computer be worth half its original value? Round answer to 1 decimal place. years
The average cost per unit, y, of producing x units of a product is modeled by y= 750,000 + 0.55x /x. Describe the company's production level so that the average cost of producing each unit does not exceed $ 8.05