Lesson 10

Rate of Change

  • Let’s calculate the rate of change of some relationships.

10.1: Growing Bamboo

The graph represents function h, which gives the height in inches of a bamboo plant t months after it has been planted.

Horizontal axis, time in months. Vertical axis, height in inches. Line graphed, Y intercept = 12. Slope =9.

  1. What does this statement mean? h(4)=24
  2. What is the value of h(10)?
  3. What is c if h(c)=30?
  4. What is the value of h(12)-h(2)?
  5. How many inches does the plant grow each month? How can you see this on the graph?

10.2: A Growing Account Balance

The balance in a savings account is defined by the function b. This graph represents the function.

horizontal axis, time in months. vertical axis, account balance in dollars. line with y intercept of 300 and slope of 100 graphed.

  1. What is . . .
    1. b(3)
    2. b(7)
    3. b(7)-b(3)
    4. 7-3
    5. \dfrac{b(7)-b(3)}{7-3}
  2. Also calculate \dfrac{b(11)-b(1)}{11-1}
  3. You should have gotten the same value, twice. What does this value have to do with this situation?

10.3: The Temperature Outside

Here are a graph and a table that represent the same function. The function relates the hour of day to the outside air temperature in degrees Fahrenheit at a specific location.

t p(t) t p(t)
0 48 6 57
1 50 7 56
2 55 8 55
3 53 9 50
4 51.5 10 52
5 52.5

Scatterplot. Horizontal axis, time in hours. vertical axis, temperature in degrees fahrenheit.

Match each expression to a value. Then, explain what the expression means in this situation.

  1. p(12)
  2. p(8)
  3. p(12)-p(8)
  4. 12-8
  5. \frac{p(12)-p(8)}{12-8}
  6. p(10)
  7. p(20)
  8. p(10)-p(20)
  9. 10-20
  10. \frac{p(10)-p(20)}{10-20}
  • 4
  • -2.75
  • 44
  • -1.4
  • 55
  • 14
  • -11
  • 38
  • -10
  • 52

Summary