The purpose of this Warm-up is for students to recall how to calculate an average rate of change from two points. Students will use this skill throughout the lesson and return to the context and data table in the last activity of the lesson.
Display the table for all to see. Ask students to describe how quickly p(t) is decreasing between 1977 (t=0) and 1978 (t=1) and then how it is decreasing between 1986 (t=9) and 1987 (t=10). (In the first year on the table it’s decreasing by 20. In the last year on the table, it decreases only by 1.5.)
Let p be the function that gives the cost p(t), in dollars, of producing 1 watt of solar power t years after 1977. Here is a table showing the values of p from 1977 to 1987.
| t | p(t) |
|---|---|
| 0 | 80 |
| 1 | 60 |
| 2 | 45 |
| 3 | 33.75 |
| 4 | 25.31 |
| 5 | 18.98 |
| 6 | 14.24 |
| 7 | 10.68 |
| 8 | 8.01 |
| 9 | 6.01 |
| 10 | 4.51 |
Which expression can be used to calculate the average rate of change in solar cost between 1977 and 1987?
10−0p(10)−p(0)
The goal of this discussion is for students to recall the meaning of average rate of change for a function and how it is calculated. Select students to describe what the value of each expression represents in this context. For example, p(10)−p(0) is the difference in cost for a solar cell between 1977 and 1987 while p(0)p(10) could be used to identify the percent change from 1977 to 1987. An important takeaway for students is that the actual expression for the average rate of change, 10−0p(10)−p(0)≈-7.55, tells us that the price decreased by -$7.55 each year on average, because the expression looks at the total difference in price between 1977 and 1987, divided by the total number of years that passed.
Some students might confuse finding an average of the values in the table and finding an average rate of change. Help them see that average usually involves one unit, such as average number of cookies. Average rate of change involves comparing how one quantity changes when another quantity changes by 1, such as cost ($) per year.
All skills for this lesson
No KCs tagged for this lesson
The purpose of this Warm-up is for students to recall how to calculate an average rate of change from two points. Students will use this skill throughout the lesson and return to the context and data table in the last activity of the lesson.
Display the table for all to see. Ask students to describe how quickly p(t) is decreasing between 1977 (t=0) and 1978 (t=1) and then how it is decreasing between 1986 (t=9) and 1987 (t=10). (In the first year on the table it’s decreasing by 20. In the last year on the table, it decreases only by 1.5.)
Let p be the function that gives the cost p(t), in dollars, of producing 1 watt of solar power t years after 1977. Here is a table showing the values of p from 1977 to 1987.
| t | p(t) |
|---|---|
| 0 | 80 |
| 1 | 60 |
| 2 | 45 |
| 3 | 33.75 |
| 4 | 25.31 |
| 5 | 18.98 |
| 6 | 14.24 |
| 7 | 10.68 |
| 8 | 8.01 |
| 9 | 6.01 |
| 10 | 4.51 |
Which expression can be used to calculate the average rate of change in solar cost between 1977 and 1987?
10−0p(10)−p(0)
The goal of this discussion is for students to recall the meaning of average rate of change for a function and how it is calculated. Select students to describe what the value of each expression represents in this context. For example, p(10)−p(0) is the difference in cost for a solar cell between 1977 and 1987 while p(0)p(10) could be used to identify the percent change from 1977 to 1987. An important takeaway for students is that the actual expression for the average rate of change, 10−0p(10)−p(0)≈-7.55, tells us that the price decreased by -$7.55 each year on average, because the expression looks at the total difference in price between 1977 and 1987, divided by the total number of years that passed.
Some students might confuse finding an average of the values in the table and finding an average rate of change. Help them see that average usually involves one unit, such as average number of cookies. Average rate of change involves comparing how one quantity changes when another quantity changes by 1, such as cost ($) per year.