1. Check it out! 3.3.2: Proving Average Rate of Change
3.3.2: Proving Average Rate of Change

2. Which boat will have the greater value in 3 years?
Lupita wants to buy a boat that will have the best resale value after 3 years.
At one boat dealer, she found a boat she likes that sells for $15,000 and depreciates at a rate of 30% per year. What will be the value of the boat after 3 years?
At another dealer, she found a boat that costs $12,000 and depreciates at a rate of 20% per year. What will be the value of the boat after 3 years?
Which boat will have the greater value in 3 years?
Common Core Georgia Performance Standard: MCC9–12.F.IF.6; MCC9–12.F.LE.1a
3.3.2: Proving Average Rate of Change

3. Create a table to show the decrease in value for the first 3 years.
At one boat dealer, she found a boat she likes that sells for $15,000 and depreciates at a rate of 30% per year. What will be the value of the boat after 3 years?
When the boat is new, it is worth $15,000; then it depreciates at a rate of 30% each year.
Create a table to show the decrease in value for the first 3 years.
3.3.2: Proving Average Rate of Change

4. Boat A will be worth $5,145 after 3 years.
Value of Boat A, in dollars ($)
15,000 1
15,000(0.70) = 10,500 2
10,500(0.70) = 7350 3
7350(0.70) = 5145
3.3.2: Proving Average Rate of Change

5. Create a table to show the decrease in value for the first 3 years.
At another dealer, she found a boat that costs $12,000 and depreciates at a rate of 20% per year. What will be the value of the boat after 3 years?
When the boat is new, it is worth $12,000; then it depreciates at a rate of 20% each year.
Create a table to show the decrease in value for the first 3 years.
3.3.2: Proving Average Rate of Change

6. Boat B will be worth $6,144 after 3 years.
Value of Boat B, in dollars ($)
12,000 1
12,000(0.80) = 9600 2
9600(0.80) = 7680 3
7680(0.80) = 6144
3.3.2: Proving Average Rate of Change

7. Which boat will have the greater value in 3 years?
Boat A will be worth $5,145 after 3 years.
Boat B will be worth $6,144 after 3 years.
Boat B will be worth more than Boat A after 3 years.
Connection to the Lesson
Students will be asked to calculate the average rate of change of a function over a specified interval given a graph.
Students will compare rates of change over various intervals.
3.3.2: Proving Average Rate of Change