Rates of Change

Key Questions

• How does rate of change relate to slope?

  Answer:

  As below.

  Explanation:

  Slope is the ratio of the vertical and horizontal changes between two points on a surface or a line.
  The vertical change between two points is called the rise, and the horizontal change is called the run.
  The slope equals the rise divided by the run: .
  This simple equation is called the slope formula.

  

  If #y = f(x+h) = 3 (x + h)^ 2#, (Just plug x + h in for x). So, you get this:

  

  The instantaneous rate of change, or derivative, can be written as dy/dx, and it is a function that tells you the instantaneous rate of change at any point.

  #y' = f'(x+h) = (d/(dx)) (3*(x)^2) = 6x * 1 = 6x#

  . For example, if x = 1, then the instantaneous rate of change is 6.

  Rate of Change Formula helps us to calculate the slope of a line if the coordinates of the points on the line are given. ... If coordinates of any two points of a line are given, then the rate of change is the ratio of the change in the y-coordinates to the change in the x-coordinates.

  

  Hope this helps.

  sankarankalyanam · 1 · Apr 15 2018
• What is rates of change?

  Rate of change is a number that tells you how a quantity changes in relation to another.
  Velocity is one of such things. It tells you how distance changes with time.
  For example: 23 km/h tells you that you move of 23 km each hour.

  Another example is the rate of change in a linear function.

  Consider the linear function: #y=4x+7#
  the number 4 in front of #x# is the number that represent the rate of change. It tells you that every time #x# increases of 1, the corresponding value of #y# increases of 4.
  If you get a negative number it means that the #y# value is decreasing.
  If the number is zero it means that you do not have change, i.e you have a constant!

  Examples:
  

  Gió · 1 · Dec 21 2014
• How do you calculate rate of change?

  Average Rate of Change

  The average rate of change of a function #f(x)# on an interval #[a,b]# can be found by

  #("Average Rate of Change")={f(b)-f(a)}/{b-a}#

  ---

  Example

  Find the average rate of change of #f(x)=x^2+3x# on #[1,3]#.

  #f(3)=(3)^2+3(3)=18#

  #f(1)=(1)^2+3(1)=4#

  #("Average Rate of Change")={f(3)-f(1)}/{3-1}={18-4}/{2}=14/2=7#

  ---

  I hope that this was helpful.

  Wataru · 2 · Nov 13 2014

• What is rates of change?
• Can a rate of change be negative?
• Explain how speed is a rate of change?
• How do you calculate rate of change?
• How does rate of change relate to slope?
• What is the rate of change if Jenna earns $60 every #2 1/2# weeks?
• In 1999, a hot dog company had a profit of $40,000. In 2007, the same company had a total profit of $68,000. What is the average rate of change of the company's profit in dollars per year?
• How to adjust this table ?
• Question #11adf
• A candy company used 20 pints of chocolate to make 5 boxes of candy. What is the rate of pints of chocolate per box?
• An airplane rises vertically 1000 feet over a horizontal distance of 1 mile. What is the angle elevation of the airplane's path?
• A pond at a hotel holds 4,290 gallons of water. The groundskeeper drains the pond at a rate of 78 gallons of water per hour. How long will it take to drain the pond?
• A deep-sea exploring ship is pulling up a diver at the rate of 25 feet per minute The diver is 200 feet below sea level. How deep was the diver 10 minutes ago?
• It took a pet store 10 weeks to sell 80 cats What is the rate sold per week?
• A pencil company used 60 grams of rubber to make 10 pencils, which is a rate of grams per pencil?
• Suppose 4.6 liters of water come out of a faucet each minute. For how many minutes was the faucet on if 52.9 liters of water came out?
• What is the rate of change of a horizontal line?
• How do you find the rate of change between the points (-8, 5) and (24, 3)?
• Kevin's savings account balance changed from $1140 in January to $1450 in April. How do you find the average rate of change in dollars per month?
• A teacher weighed 145 lbs in 1986 and weighs 190 lbs in 2007. What is the rate of change in pounds per year?
• A plane from Dallas to Boston flies 1,558 miles in 4 hours. About how many miles does this plane fly each hour?
• It takes a car 1.75 h to go from mile marker 10 to mile marker 115. What is the average speed of the car?
• For every 1/2 mile that Sira jogs, she walks 3/4 mile. What unit rate gives the number of miles Sira jogs for every mile she walks?
• A bird flies 2/3 of a mile per minute. How many miles per hour is it flying?
• In 1980, the average price of a home in Brainerd County was $100,000. By 1986 the average price of a home was $112,000. What is the rate of change?
• A 2000 Ltank containing 550 L of water is being filled with water at the rate of 75 L per minute from a full 1600 L tank. How long will it be before the two tanks have the same amount of water?
• A bacteria doubles its population in 8 hours. At this rate how many hours would it take the population of the bacteria to triple?
• A submarine descends below the ocean's surface at a of rate 75 feet per minute. How many feet below the ocean's surface will the submarine be in 12 minutes?
• The population of a small rural town in lowa went from 5700 people in 1998 to 7945 in 2005. What is the rate of change in the population for this town?
• A scuba diver is 30 feet below the surface of the water 10 seconds after he entered the water and 100 feet below the surface after 40 seconds. What is the scuba divers rate of change?
• The temperature in St. Paul was #45^circ#F. Five minutes later it was 30°F. What was the average change in temperature in degrees per minute as an integer?
• Tinseltown wants to know if their population is in danger. Their current population is 12,000 people but in 2001 it was 15,321. What is their growth rate?
• In a particular city in one year, the birth rate is 25 per 1,000 people. The death rate per 1,000 people#color(blue)(" is 17 per 1,000 people")#. What is the city's annual population growth?
• Question #792d3
• Question #d37fd
• Question #52fb9
• At a dairy​ plant, a milk tank can be filled in 4 hours​ (using the​ in-valve). Using the​ out-valve, the tank can be emptied in 8 hours. If both valves are open and milk is being pumped into the​ tank, how long will it take to fill the​ tank?