A linear function is described either verbally, numerically, or graphically. Express f in the form f(x) = ax + b. The function has rate of change -2 and initial value 3.

Q: A function is given. fx) = x - 4x; x= 0, x = 10 (a) Determine the net change between the given…

A: See the details solution in below

Q: 55. Under what circumstances is a linear function f(x) = mx + b odd? Can a linear function ever be…

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Q: 8. According to an Insurance Company, the percentage of accidents caused by teenagers texting while…

A: A linear function in one variable that represents a line graphically. The gradient of the line is…

Q: In a study on the speed of muscle contraction in a certain species of frogs under various​ loads,…

A: Given : In a study on the speed of muscle contraction in a certain species of frogs under various​…

Q: Part A A factory begins the day with 6, 000 packaged light bulbs. The machines in the factory can…

A: This question is based on Application of linear function.

Q: A large koi pond is filled from a garden hose at the rate of 10 gal/min. Initially, the pond…

A: a) Given that initially, there was 300 gal of water.  And water is entering at a rate of 10 gal/min.…

Q: Let f(x) = (x + 5)² and g(x) = 1 – 5x. (a) Only one of the two functions f and g is linear. Which…

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Q: By noon, 3 inches of rain had fallen during a storm. Rain continued to fall at a rate of inch per…

A: We will find the amount of rainfall.

Q: Let f be the linear function f(x) = -2x + 5. (a) The rate of change of f is (b) The graph of f is a…

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Q: 2. Let f be the linear function f1x2  5x  7 .(a) The rate of change of f is .(b) The graph of f…

A: Solution:          Linear functions are those whose graph is a straight line. Linear function has…

Q: In 1983, the bison population in Yellowstone National Park was estimated to be only 50 animals…

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Q: A local fruit company recently released a new flavor of applesauce. By the end of the first year,…

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Q: (a) Find an equation for the family of linear functions with slope 2 and sketch several members of…

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Q: U.S. Airplane Passenger Projections  In a report issued by the U.S. Department of Transportation in…

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Q: In 2000, the life expectancy of females born in a certain country was 79.7 years. In 2008, it was…

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Q: On a certain route, an airline carries 6000 passengers per month, each paying $200. A market survey…

A: On a certain route, an airline carries 6000 passengers per month, each paying $200. A market survey…

Q: use linear functions. The linear depreciation method assumes that an item depreciates the same…

A: Consider the given information. The general form of the linear function is defined as. y=mt+c Where,…

Q: A hot air balloon launches straight up into the air from the top of a hill with an elevation of 200…

A: Given time=t, elevation = E Given that at t=0 minute, h=200 feet At t=20 minute, h=620 feet So two…

Q: The graph of a linear function f is given. (a) Find the rate of change of f. (b) Express f in the…

A: Linear functions are functions with linear relationship between the dependent variable y and…

Q: The water level in a glass decreases 0.4 cm each hour due to evaporation.  At the beginning of the…

A: The general equation of a straight line is y = mx + c, where m is the gradient, and y = c is the…

Q: Let x represent the number of years after 1970. Find a formula in slope intercept form for a linear…

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Q: Find the slope of the function f (x) = x 3 + 3x 2 + 3x + 1 at x = 0 1 0 3

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Q: The graph of a linear function f is given. (a) Find the rate of change of f. (b) Express f in the…

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Q: A large koi pond is filled from a garden hose at the rate of 19 gal/min. Initially, the pond…

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Q: The table to the right lists the annual hours worked by the average worker in a country for selected…

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Q: You invest $1,000 in a certificate of deposit (CD) that earns 5% interest every year. If the…

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Q: A manufacturer of a particular item has monthly fixed costs of $500 and variable costs of $15 per…

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Q: 3. An investment of $2000 in a bank account doubles every 5 years. The function that models the…

A: Given f(x) = 2000·2x where x is the number of doubling periods.

Q: A function is given (either numerically, graphically, or algebraically). Find the net change and the…

A: Given: f(x) = x2 - 2x To find the net change, Net change=f4-f1 Now we find f(4) as,…

Q: By noon, 4 inches of rain had fallen during a storm. Rain continued to fall at a rate of inch per…

A: Given:

Q: Which function models the population of Metropolis x years after 2000?

A: Given initial population = 2,600,000 Decreasing at rate of 1.1%

Q: Let f(x)=x2+x−12f(x)=x2+x-12. Find the average rate of change in ff over the interval [0,3][0,3].…

A: The average rate of change of a function f(x) over an interval a,b is given by f(b)-f(a)b-a.

Q: Persons taking a 30-hour review course to prepare for a standardized exam average a score of 620 on…

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Q: A manufacturer of a particular item has monthly fixed costs of ​$700 and variable costs of ​$25 per​…

A: Given: A manufacturer of a particular item has monthly fixed costs of ​$700 and variable costs of…

Q: Assume that the growth of the membership of a country club was linear from 1996 to 2000 with a…

A: The growth of the membership of a country club was linear from 1996 to 2000 with a membership of 232…

Q: A local fruit company released a new flavor of applesauce. After 1 year, the profits on this product…

A: NOTE: Refresh your page if you can't see any equations. . after 1 year, the profit was $29000 after…

Q: A table of values for a linear function f is given. f(x) 9. 4 12 15 8. 18 (a) Find the rate of…

A: Solve

Q: World grain production was 1,241 million tons in 1975 and 2,048 million tons in 2005, and has been…

A:

Q: The water level in a glass decreases 0.4 cm each hour due to evaporation. At the beginning of the…

A: Part A Let y represent water level, x represent time and 0.4cm/hour is the rate of evaporation. So…

Q: (a) Find an equation for the family of linear functions with slope 2 and sketch seceral members of…

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Q: Find the linearization of the function at x = a = -4

A: Since the function is not given so i have assumed the function as f(x)

Q: Consider the function f(x)= 6/ +2 on the interval 1, 6). Find the average or mean slope of the…

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Q: A large koi pond is filled from a garden hose at the rate of 18 gal/min. Initially, the pond…

A: It is given that the garden hose is filling with water at a rate of 18 gal/min. The initial volume…

Q: Water is being pumped into a swimming pool at the rate of 5 gal per min. Initially, the pool…

A:

Q: In a study on the speed of muscle contraction in a certain species of frogs under various loads,…

A: (A) Here, the approaching value of v(x) is the limiting value of v(x) when x tends to infinity.

Q: A roof has a 0.3-inch layer of ice on it from a previous storm. Another ice storm begins to deposit…

A: Given. A roof has a 0.3 inch layer of ice on it from a previous storm. Another ice storm begins to…

Q: In a study on the speed of muscle contraction in a certain species of frogs under various loads,…

A: To find that the number to which v(x) approaches as x increases

Q: Consider the function that assigns to each number x the value 3x^2 (three x to the second power).…

A: Given that input(x) output (3x2) -2   -1   0   1   we have to find the following

Q: ff and g are functions of time, and at time t = 3, f equals 9 and is rising at a rate of 4 units per…

A: Given at time t =3, f(t) =9 and g(t) = 5. Also, f't=4 and g't=9.   We have since gt≠0,fgt=ftgt and…

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.