calculating average rate of change we will be working on word problems today that require you to do...
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Calculating Average Rate of Change
We will be working on word problems today that require you to do the
following three things:(1)Determine the coordinates of two
points(2)Find the average rate of change, a.k.a. SLOPE between those points(3)Write a sentence explaining the
situation using units in your answer.
Calculating Average Rate of Change
COMMON CORE
#4, #28, #30
Calculating Average Rate of Change
(1) The population of Austin, Texas in 1990 was 472,000 people, The population in 1980 was 346,000.
Find your coordinates.So (1980, 346,000) & (1990, 472,000)Use the AOC formula,
Calculating Average Rate of Change
(1980, 346,000) & (1990, 472,000)So 472,000 – 346,000 1990 – 1980 126,000 10 12,600 So from 1980 to 1990, the city of Austin
had a population increase of 12,600 per year.
Calculating Average Rate of Change
What would happen if you swapped points?
(1990, 472,000) & (1980, 346,000)And used the AOC formula.
Nothing except your answer would be two negatives which is still a
positive rate of change.
Calculating Average Rate of Change
(2) At 11:00AM Sharon passes mile marker 295 on highway 35. At 2:00PM she passes mile marker 475.
Find your coordinates.So (11, 295) & (14, 475)Use the AOC formula,
Calculating Average Rate of Change
(11, 295) & (14, 475)So 475 – 295 14 – 11 180 3 60 So from 11:00AM to 2:00PM, Sharon
averaged 60 miles per hour on highway 35.
Calculating Average Rate of Change
(3) Juan joined a gym to lose weight. After three weeks, he weighed 189 pounds. Juan was down to 162 pounds when he had been a member for twelve weeks.
Find your coordinates.So (3, 189) & (12, 162)Use the AOC formula,
Calculating Average Rate of Change
(3, 189) & (12, 162)So 162 – 189 12 – 3 -27 9 -3 So Juan lost an average of three pounds per
week over this nine week period.
Calculating Average Rate of Change
Work these problems together as a group and we will check each shortly.
(4) In 1984, the price of a VCR was $375. By 1996, the price was $125.
Write your coordinates, find the AOC, and write a sentence explaining the situation.
Calculating Average Rate of Change
(4) In 1984, the price of a VCR was $375. By 1996, the price was $125.
(1984, $375) & (1996, $125)-$25 The value of a VCR decreased $25 per
year over the twelve year period.
Calculating Average Rate of Change
Work these problems together as a group and we will check each shortly.
(5) When an amusement park opens, the counter on the turnstile at the entrance read 1278. Seven hours later, the counter read 3672.
Write your coordinates, find the AOC, and write a sentence explaining the situation.
Calculating Average Rate of Change
(5) When an amusement park opens, the counter on the turnstile at the entrance read 1278. Seven hours later, the counter read 3672.
(0, 1278) & (7, 3672)342 342 people per hour entered the
amusement park during the first seven hours it was open.
Calculating Average Rate of Change
Work these problems together as a group and we will check each shortly.
(6) At 11:00AM, the temperature outside was 56˚F. By 8:30PM, the temperature was 34˚F.
Write your coordinates, find the AOC, and write a sentence explaining the situation.
Calculating Average Rate of Change
(6) At 11:00AM, the temperature outside was 56˚F. By 8:30PM, the temperature was 37˚F.
(11, 56) & (20.5, 37)-2The temperature dropped an average
of 2 degrees Fahrenheit over the 9.5 hour period.
Calculating Average Rate of Change
Work this problem by yourself and show it to me when you are finished.
(7) Dub left Austin with an odometer reading 12,584 and a full tank of gasoline. When she stopped in Houston, the odometer read 12,788. She spent $31.12 to fill the tank completely up with eight gallons of gas. THERE ARE MULTIPLE WAYS TO DO THIS!