5.
The steepness of the roof of a house is referred to as the pitch of the roof by home builders.
6.
Give one reason why some homes have roofs which have a greater pitch . There is less snow buildup in the wintertime.
7.
Engineers refer to the rate of change of a road as the grade .
8.
They often represent the rate of change as a percentage .
9.
A grade of 8% would mean for every rise of 8 units there is a run of 100 units . = 8% 8 100 Rate of change =
10.
The steepness of wheelchair ramps is of great importance for safety. Rate of change of wheelchair ramp = 1 12 If the rise is 1.5 m, what is the run? Answer: 18 m because
11.
3 m 5 m Determine the rate of change ( pitch ) of the roof.
12.
Determine the rate of change of each staircase. 2 3 3 3
13.
Determine the rate of change. Which points will you use to determine rise and run? = $5/hr 20 4 Earnings Number of Hours Worked What does this rate of change represent? The hourly wage
14.
REAL LIFE
Mr. and Mrs. Overjoyed had a healthy baby girl named Joy who weighed 7.5lbs. at birth. At the end of 4 months, the baby weighed 13.5lbs.
How fast did her weight change from birth to 4 months?
15.
REAL LIFE (PART 2)
To answer this question, we calculate the Rate of Change of Joy’s weight, that is, how much she gained per month.
Change in weight 13.5lbs – 7.5lbs 6lbs
Change in age 4mo – 0mo 4mo
1.5lbs./month
16.
POSITIVE RATE OF CHANGE
At age 6 months, Joy weighed 15.75lbs.
How fast did she grow from 4 months to 6 months?
17.
Line Graph: Rate of Change
18.
NEGATIVE RATE OF CHANGE
Joy was gaining weight, so the rate of change was positive. But a rate of change can be negative.
Let’s take a look at the population of Chicago from 1830 to 2000…
19.
The rate of change, in people per year, from 1890 to 1900. For these years, the population increased.
Change in population 1,698,575 – 1,099,850 598,725p
Change in years 1900 – 1890 10yr
59, 872.5 people/year
20.
Between 1970 and 1980 the population decreased, so the rate of change is negative.
Change in population 3,005,072 – 3,369,357 -364, 285 p
Change in years 1980 - 1970 10 years
- 36,428.5 people per year
21.
22.
FORMULA FOR RATE OF CHANGE
y2 – y1
x2 – x1
The rate of change between points (x1, y1) and (x2, y2)