# 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.

- What does this statement mean? \(h(4)=24\)
- What is the value of \(h(10)\)?
- What is \(c\) if \(h(c)=30\)?
- What is the value of \(h(12)-h(2)\)?
- 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.

- What is . . .
- \(b(3)\)
- \(b(7)\)
- \(b(7)-b(3)\)
- \(7-3\)
- \(\dfrac{b(7)-b(3)}{7-3}\)

- Also calculate \(\dfrac{b(11)-b(1)}{11-1}\)
- 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 |

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

- \(p(12)\)
- \(p(8)\)
- \(p(12)-p(8)\)
- \(12-8\)
- \(\frac{p(12)-p(8)}{12-8}\)
- \(p(10)\)
- \(p(20)\)
- \(p(10)-p(20)\)
- \(10-20\)
- \(\frac{p(10)-p(20)}{10-20}\)

- 4
- -2.75
- 44
- -1.4
- 55
- 14
- -11
- 38
- -10
- 52