# 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.

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.

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

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