The country A Consumer Price Index is approximated by the following​ formula, where t represents the number of years after 1990.   A(t)=100e0.027t   For​ instance, since​ A(16) is about 154​, the amount of goods that could be purchased for​ $100 in 1990 cost about $154 in 2006. Use the function to determine the year during which costs will be 95​% higher than in 1990.

Q: (a) Write a formula for the cost, C, of renting a car as a function of the number of days, d, and…

A: Solution

Q: Total expenditures in a country (in billions of dollars) are increasing at a rate of f(x) =…

A: a)Given rate of total expenditure f(x)=8.68x+87.14let f(x) be the total…

Q: The cost of a telephone call from Mendocino to San Francisco during business hours is 40 cents for…

A: Given that the cost of a telephone call from Mendocino to San Francisco during business hours is 40…

Q: 1. The function f(x) = 70x² can be used to estimate the BMR of mammals and many other types of…

A: The function that used to estimate the BMR (Basic Metabolic Rate) of mammals is f(x)=70x34. where x…

Q: Researchers fit data from over 6000 fetal ultrasounds. They measured the femur length, L, (in…

A:

Q: 1. Johana works in the crime lab at the New York City · Police Department. A woman's shoe was found…

A: Here a function which represents the relationship between height of the woman and the shoe size of…

Q: In this exercise, a verbal description of a function is given. Use a formula to express the…

A: Given: The selling price of lemonade is 75 cents per glass. Investment is $ 2.00 in the ingredients.…

Q: Poverty The passage of the Social Security Amendments of 1965 resulted in the creation of the…

A: The derivative gives the rate of change of some variable with respect to other quantity. If there is…

Q: We are constructing a box from a rectangular piece of cardboard. The piece of cardboard which…

A: As per our guidelines, we can answer only three sub-parts in a single request. Kindly re-post the…

Q: D An amusement park charges $11 for admission. On average, 20,000 people visit the park each day,…

A: Given that, Admission charge=$11 people visited the park on one day =20,000 suppose they increase…

Q: The bar graph shows your chances of surviving to various ages once you reach 60.The functions f(x) =…

A: Substitute the value of x=90 in f(x) =-2.9x+286. It means that the chance of a 60 year old…

Q: The height of stacked chairs s chairs are si inches high 3 chairs are 45 inches high 8 chairs are 60…

A:

Q: A ball is thrown in the air from the top of a science I building from Modesto Junior College. Its…

A:

Q: From 2005 through 2010, an Internet sales company was hiring new employees at a rate of n(x) = 588 +…

A: We need to find function.

Q: Medicine Concentration The concentration C of amedication in the bloodstream t hours after…

A: Given function is Ct=-0.002t4+0.039t3-0.285t2+0.766t+0.085. a. Graph the above equation and obtain…

Q: A cannon is placed on the edge of a cliff. The height of a fired cannonball is modeled by the…

A: We will find how long the cannonball was in the air as following .

Q: Using a model of the prototype ball thrower, a ball is fired into the air with an initial upward…

A: Given that height of the ballht=-16t2+48t+41.if balls reaches maximum height then…

Q: Total expenditures in a country (in billions of dollars) are increasing at a rate of f(x) = 9.02x +…

A:

Q: SOLVE USING PIECEWISE FUNCTION A computer cafe charges their customer $40 per hour, a $10 discount…

A: Let's solve.

Q: a. Create two functions using the following guidelines: i. one is represented as an equation, one as…

A:

Q: A manufacturing plant earned $80 per man-hour of labor when it opened. Each year, the plant earns an…

A: If you like the solution then please give it a thumbs up..... The Answer is:         Equation:…

Q: - The function P(x) important features of a classroom lecture as a function of time, where x…

A:

Q: The bar graph shows your chances of surviving to various ages once you reach 60. The functions f(x)…

A: Given that: The functions  f ( x) = - 2.9x + 286   and g ( x) = 0.01 x 2 - 4.9x  + 370.

Q: Going Green The average top-loading washing machine uses about 40 gallons of water per load of…

A: Solution: Consider the given that  The average uses per load about 40 gallons of water. Let W be the…

Q: a) Give the function that describes the height of the rocket in terms of time t. b) Determine the…

A: Given that  Height of the buliding is 144feet  Initial velocity 203feet per sec  To find the time…

Q: 1. The function f(x) = 70x² can be used to estimate the BMR of mammals and many other types animals.…

A: Given the parent function: hx=x34

Q: Women in the Workforce Using data starting with1950 and projected to 2050, the number of women(in…

A: Given: The number of women(in millions) in the workforce is given by the functionP = 0.79x + 20.86,…

Q: A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 13…

A: NOTE: Refresh your page if you can't see any equations. . here the length of the cardboard is…

Q: 2. A rocket is launched in the air. Its height, in meters above sea level, as a function of time, in…

A: Given that a rocket is launched in the air. Its height , in meters above sea level as a function of…

Q: An amusement park charges $10 for admission. On average, 25,000 people visit the park each day…

A: Given: The amusement charges $10 for admission. Number of peoples visit the part every day=25000. If…

Q: Consumer expenditures, in millions of dollars, on all types of books in the United States for the…

A:

Q: A movie theater is filled to capacity with 250 people. After the movie ends, people start leaving at…

A: agiventotal capacity=250 peopletherate of people start leaving=50 each minutenumber of people…

Q: 8. A thermometer reading 20°F is brought into the room where the temperature is 80°F, two minutes…

A:

Q: Minimizing Average Cost The total monthly cost (in dollars) incurred by a certain guitar…

A:

Q: Ultrasound is often used to make images of developing fetuses. In particular, by measuring the size…

A: GIVEN: L = -37. 50 + 3.17t - 6.33 x 10-4 t3

Q: Ultrasound is often used to make images of developing fetuses. In particular, by measuring the size…

A: The femur length is given as , L=-37.50+3.71t-6.33×10-4t3 where t is fetus age in weeks.

Q: You are designing a box without a top by cutting squares of equal size from the corners of a piece…

A:

Q: PART II II. Suppose that the total worldwide sales for a song album are approximated by the…

A: Gross sales are the grand total of sale transactions within a certain time period for a company. Net…

Q: The wage gap is used to compare the status of women’s earnings relative to men’s. The wage gap is…

A: Given the function and graphs for wage gap : Gx=-0.01x2+x+60

Q: An amusement park charges $11 for admission. On average, 20,000 people visit the park each day.…

A:

Q: Total expenditures in a country (in billions of dollars) are increasing at a rate of f(x) =…

A:

Q: . Gold Prices The price of an ounce of gold in U.S. dollars for the years 1997–2011 can be modeled…

A: Given  G(x) = 11.532x2 - 259.978x + 1666.555

Q: An aircraft factory manufactures airplane engines. The unit cost  C  (the cost in dollars to make…

A: It is given that the unit cost for x number of engines are  Cx=0.7x2-154x+23656. To obtain the…

Q: A fence is to enclose a rectangular vegetable farm with an area of 400 square meters. If x is the…

A:

Q: The bar graph shows your chances of surviving to various agesonce you reach 60.The functions f(x) =…

A: Given that, fx=-2.9x+286g(x)=0.01x2-4.9x+370

Q: Inflation An antique table increases in value according to the function v(x) = 850(1.04x)…

A: An antique table increases in value according to the function v(x) = 850(1.04x) dollars,where x is…

Q: The area of an equilateral triangle with sides of length x is given by the function V3 defined by…

A: Follow 2nd step.

Q: The circumference of a circle is given by the formula 2πr, where r is the radius of the circle. A…

A:

Q: In this exercise, a verbal description of a function is given. Use a formula to express the…

A: Let n be the number of glasses of lemonade sold. The price per glass is 75 cents. To find the…

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.