1. I Can See—Can’t You? 2.7H Date: 10/08/18
1. Grab your Binder 2. Copy down the Essential Question (EQ). 3. Work on the Warm-up.
Essential Question
How is average rate of change different from instantaneous rate of change
Warm Up:

2. Purpose
The purpose of this task is to introduce students to the idea of the average rate of change of a function in a given interval.

3. Kwan’s parents bought a home for $50,000 in 1997 just as real estate values in the area started to rise quickly. Each year, their house was worth more until they sold the home in 2007 for $309,587.
Model the growth of the home’s value from 1997 to 2007 with both a linear and an exponential equation. Graph the two models below.
Linear model:
Exponential model:

4. Kwan’s parents bought a home for $50,000 in 1997 just as real estate values in the area started to rise quickly. Each year, their house was worth more until they sold the home in 2007 for $309,587.
Model the growth of the home’s value from 1997 to 2007 with both a linear and an exponential equation. Graph the two models below.
Linear model:
Exponential model:

6. The average rate of change is defined as the change in y (or f(x)) divided by the change in x. 3. What was the average rate of change of the linear function from 1997 to 2007? 4. What is the average rate of change of the exponential function in the interval from 1997 to 2007? 5. How do the average rates of change from 1997 to 2007 compare for the two functions? Explain.

7. 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑐ℎ𝑎𝑛𝑔𝑒= 𝑓 𝑦 2 −𝑓( 𝑦 1 ) 𝑓 𝑥 2 −𝑓( 𝑥 1 ) 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑐ℎ𝑎𝑛𝑔𝑒= Slope of the secant line

9. 6. What was the average rate of change of the linear function from 1997 to 2002? 7. What is the average rate of change of the exponential function in the interval from 1997 to 2002? 8. How do the average rates of change from 1997 to 2002 compare for the two functions? Explain.

10. Lets Learn some Calculus

12. Module 2 Review Day 1 Date: 10/09/18
1. Grab your Binder. 2. Get out your Module 2 Review Packet. 2. Copy down the Essential Question (EQ). 3. Work on the Warm-up.
Essential Question
How is the common difference relate to the slope and average rate of change?
Warm Up:
Work on your review packet

13. Gallery Walk
There are different station, where a student will have their work display.
Other students, in groups of 3, will walk around and look at then station solution.
At each station, the other students can ask question to station student.
The station student has to explain and answer any question that relates to the problem.

14. Map of the class room

15. Display Question 1

16. Isaac started a race at 500 meters
Isaac started a race at 500 meters. He wants to starting cover more distance at a rate of 5% per minute.
𝑝 0 = more distance 5% 𝑟=1+.05=1.05
I. Write an explicit exponential function to model Isaac running space. Use 𝑡 for time and 𝑃(𝑡) for the values of the item.
0−𝑡𝑒𝑟𝑚 𝑒𝑞𝑎𝑢𝑡𝑖𝑜𝑛 𝑃 𝑡 =𝑝 0 𝑟 𝑡
Solution 𝑃 𝑡 =500 (1.05) 𝑡
II. What will her distance after 3 minutes? Round your answer to the nearest cent.
3 minutes is when 𝑡=3
𝑃 3 =500 (1.05) 3
𝑃 𝑡 ≈ 𝑚𝑒𝑡𝑒𝑟𝑠
Isaac decided to look up a competitor race time online and found this information:
He believes this could be modeled by a linear function. Do you agree; Yes or No? Explain your reasoning?
Yes, I agree because there is a common difference of 25 minutes per 1 meter
Distance (meters) 1 2 3
Time (minutes)
500
525
550

17. Display Question 2

18. 2. Multiple Choices: What is the growth ratio of an exponential function curve which passes through the point (0,2) and (5,486)? *Make a chart to make it easy to look at* Method 1: Guess and check Method 2: Equation 𝑓 𝑥 =𝑓(0) 𝑟 𝑥 486=2 𝑟 5 243= 𝑟 5 ( 243) 1 5 = 𝑟 5 5 3=𝑟 𝒏 1 2 3 4 5
𝑓(𝑛)
486

19. Display Question 3

20. 3. An online bidding store recorded and tracked a purse that was auction off.
Select all statements which are true. Blue is correct, Red is incorrect
The initial bid was $60
Online bidding for the purse increase by $5 for each bid
The relationship between the bid number and bid amount is continuous.
The bid amount will be $100 on the 10 bid number.

21. Display Question 4

22. 4. Determine whether the relationships being represented is Linear, Exponential or Neither.
Indicate your answer by selecting on the appropriate box.
Linear
Exponential
Neither
A volleyball tournament begins with 128 teams. After the first round, 64 teams remain. After the second round, 32 teams remain.
The total number of babies born in a country each minute after midnight January 1st can be estimated by the sequence shown in the table.

23. Display Question 5

24. A forest fired started and the Fire chief notice that the fire area started with only 20 acres. As time goes on the fire grows by a factor of 2 every hour. Assume the relationship between the hours and the acres of fire are continuous. Which of the following functions describes this relationship? 𝑓 0 =20 𝑟=2 𝑓 𝑥 =𝑓(0) 𝑟 𝑥 0 term equation 𝑓 𝑥 =20 (2) 𝑥 Plug in values

25. Display Question 6

26. A relationship is shown between the number of student on doing homework and the number of problem they are getting done.
There is a common difference of 4 problems done for every addition 1 student.
Students
Problems done 1 4 2 8 3 12 16

27. Display Question 7

28. Multiple Choices: Mrs. Owen owns a house in Fontana
Multiple Choices: Mrs. Owen owns a house in Fontana. The restate company determines the value of Mrs. Owen house each year. The exponential function 𝑆 𝑡 =400 (1.05) 𝑡 models the relationship between the value, H, in thousands of dollars, of the house and the number of years, t, since Mrs. Own bought the house. Which statement correctly interprets his model? ( ) The value of the house increase by 1.05% each year. ( )The value of the house increase by 5% each year. ( )The value of the house increase by $1,050 each year. ( )The value of the house increases by $5,000 each year. All the answer is asking about the growth factor. Remember growth factor is 𝑟=1+𝑑𝑒𝑐𝑖𝑚𝑎𝑙 1.05=1+𝑑𝑒𝑐𝑖𝑚𝑎𝑙 .05=𝑑𝑒𝑐𝑖𝑚𝑎𝑙 growth factor 5%=𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒

29. Display Question 8

30. Richard buys a new laptop for $1,800
Richard buys a new laptop for $1,800. The laptop depreciates in value by 8% each year. Write an exponential model to represent this situation. Use the variable y to represent the value of the car after t years. 𝑓 0 =1,800 0-term for a new laptop Depreciate ( decay) is when r = r = .92 𝑦=𝑓(0) 𝑟 𝑥 0-term Expeontial equation 𝑦=1,800 (.92) 𝑥 0-term Expeontial equation

31. Display Question 9

32. Determine whether the following situations are discrete or continuous
Determine whether the following situations are discrete or continuous. Mark your answer by clicking on the appropriate box.
Discrete
Continuous
Jack has 12 bags of Hot Cheetos. Every day, he eats one bag. The relationship between days and the Hot Cheetos …
Domain is days, Range is bag of Cheetos
A deadly virus is release into a population, the amount of people infected is reported to triple each minute. The relationship between minute and the infected people is …
Domain is minutes, Range is Infected people
Cherry blossoms fall at a rate of 5 centimeter per second. The relationship between second and centimeter is…
Domain is second, Range distance

33. Question 10 is removed This is a compound interest problem
𝑦=𝑷 (1+ 𝑟 𝑛 ) 𝑛𝑡
𝑷=𝟐,𝟎𝟎𝟎 𝒑𝒆𝒐𝒑𝒍𝒆
r=.04
n=12 because its monthly
𝑡=1 𝑦𝑒𝑎𝑟
𝑦=𝟐,𝟎𝟎𝟎 ( ) 12∙1
𝑦≈2049 people

34. Display Question 11

35. x
f(x) 1 2 7 x
g(x) 1 2 7

36. x f(x) 1 2 7 x g(x) 1 2 7 Common ratio is 7 𝑜𝑟 7 1 2 𝑔 𝑥 =𝑔(0) 𝑟 𝑥1 2 7 x
g(x) 1 2 7
Common ratio is 7 𝑜𝑟
𝑔 𝑥 =𝑔(0) 𝑟 𝑥
7=1 𝑟 2
7 =𝑟
Common difference is 3
𝑚= 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1
𝑚= 7−1 2−0
𝑚=3

37. 𝑓 𝑥 =3𝑥+1 𝑔 𝑥 =1( 7 ) 𝑥

38. Display Question 12

39. A car initially costs $32,000 and depreciates at a rate of 20% of its value every year. How much will the car be worth four years after it was purchased? 𝑓 0 =$32,000 0-term for a new laptop Depreciate ( decay) is when r = r = .80 f(x)=𝑓(0) 𝑟 𝑥 0-term Expeontial equation f(x)=32,000 (.80) 𝑥 0-term Expeontial equation f(x)=32,000 (.80) 4 for the fourth year f(4)=13,107.2

40. Richard buys a new laptop for $1,800
Richard buys a new laptop for $1,800. The laptop depreciates in value by 8% each year. Write an exponential model to represent this situation. Use the variable y to represent the value of the car after t years. 𝑓 0 =1,800 0-term for a new laptop Depreciate ( decay) is when r = r = .92 𝑦=𝑓(0) 𝑟 𝑥 0-term Expeontial equation 𝑦=1,800 (.92) 𝑥 0-term Expeontial equation

41. Display Question 13

42. The line graphed on the coordinate plane below shows the relationship between the distance (meters) and time ( second) a runner record for his/her speed (meter per second). What is the runner speed in meter per second?

43. Display Question 13 What is the runner speed in meter per second?
𝑚= ∆𝑦 ∆𝑥 average speed
𝑚= 2 𝑠𝑒𝑐𝑜𝑛𝑑 4 𝑚𝑒𝑡𝑒𝑟𝑠
𝑚= 1 𝑠𝑒𝑐𝑜𝑛𝑑 2 𝑚𝑒𝑡𝑒𝑟𝑠
speed is 2 meters per 1 second