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 is 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