Modeling with Trigonometry Application
2-9-21 Assignment
Goals:
  1. Use a given model to determine the implied given through the function itself
  2. Describe behavior of the given model with points 
  3. Use intervals to describe specific behavior from a model 

2-9-21 HWK
​ Videos and solutions
Lakeside Town Population

Question 1:
​What is the average population of the town for the entire year?

8000 people
Question 2:
​What is the maximum population for this town? 
​When does this maximum occur? 

13000 People 
x = 10
End of October/Beginning of November 
Question 3:
By how much does the town’s population change over the course of the year? 

Range 10000 people 
Range [3000,13000]
the population varies by +/- 5000 people from the average of 8000 people
Question 4:
What is the minimum population for this town? 
When does this minimum occur? 

3000 people
x = 4
End of April/ Beginning of May
Question 5
Over what months does the population exceed 7000?  (use intervals) 

x E [0,1.385) U (6.615,12 ]
0 < x <  1.385  OR  6.615 < x < 12
Jan 1 to mid February  (2/11)
Past midway of July (7/20-7/21) to  Dec 31
Question 6: 
Over what months does the population fall below 4000?  (use intervals) 

x E (2.771, 5.229) 
2.771 <  x  < 5.229
Almost March 24 <  x <  Almost June 7

2-9-21 HWK
​ Videos and solutions
Tourist Attraction Population

Question 7:
What is the “average” number of visitors for the tourist attraction for the entire year during any one month? 

4.1 Million
4,100,000 million
Question 8: 
What is the maximum number of visitors for this tourist attraction? 
​
​When does this maximum occur over the course of the three-year study? 
 



6.4 Million or 6,400,000
​
February of each of the years studied  x = 2
                                                             x = 12+2 = 14 
                                                             x = 24+2 = 26  
Question 9:
By how much does the number of visitors change over the course of the three-year study? 

4.6 million range  [1.8, 6.4]       

​varies by no more than 2.3 million from 4.1 million avg pop
Question 10:
What is the minimum number of visitors for this tourist attraction?  
When does this minimum occur over the course of the three-year study? 

1.8 million or 1,800,000

August of each year
x = 8   x = 8+12 =20  x = 8+24 = 32

Question 11:
Over what months does the population exceed 6000000?  (use intervals) 

NOTE: 6,000,000 = 6.0 on this scale   

​x E (0.86, 3.14) U (12.86, 15.14) U (24.86, 27.14)

 0.86 < x < 3.14 OR
12.86 < x < 15.14  OR
24.86 < x < 27.14
Question 12:
Over what months does the population fall below 5.2 million?  (use intervals) 

x E (4.048, 11.95) U (16.048, 23.95) U (28.048, 35.95)

4.048 < x < 11.95 OR
16.048 < x < 23.95 OR
28.048 < x < 39.95

2-9-21 HWK
​ Videos and solutions
Voltage Problem

Question a)
What is the period of the current in Canada?

1/60 of a second
Question b)
Graph and Label Voltage Function

y axis = Voltage
x axis = seconds 
Question c)
When is the voltage at 110V (the amount required to turn on the heat lamp) for the first time?

0.0019 seconds 

2-9-21 HWK
​ Videos and solutions
Lasso Problem

Question a)
What is the highest point reached by the knot?

6.5 feet above the ground
Question b)
What is the lowest point reached by the knot?

0.5 feet above the ground
Question c)
What is the period?

1.2 seconds or 6/5 seconds
Question d) 
​Find the height of the know after 25 seconds

2 feet above the ground