Download AFM Unit 1 Linears Day 7 Linears Review

AFM Unit 1 Review
Name_________________________________________
1a.
1b.
1c.
A is the independent variable, n is the dependent variable
Domain {0, 250, 500, 750, 1000, 1250, 1500}
Range {0, 1, 2, 3, 4, 5, 6}
yes, linear, because the rate of change (slope) is constant.
1
The equation is: Y = 250n + 0
2a.
2b.
2c.
𝑃𝐴 , 𝑃𝐵 , 𝑃𝐷
Towns A and B have the same populations in t= 21.428 years.
Town A has an initial population of 10,000 people and is increasing by 1,800 people per year.
Town B has an initial population of 55, 000 people and is decreasing by 300 people per year.
3a.
3b.
The cost of producing 120 units would be $11,100
The fixed cost before production is $10,500
The unit cost is $5 per unit/computer produced
4a.
4b.
The Artic Refrigerator $1,000 compared to $750
They will have the same value after 13 years.
5a.
5b.
Y = 80 + 30t
Y = 120 + 20t
The money spent will be equal after 4 months
6a.
6b.
Not Linear
3
Linear Y = 4 𝑥 − 1
7a.
7b.
7c.
7d.
7e.
Y = − .42x + 88.1
The slope is −.42, which represents the decrease in bench-presses per lb. increase in weight.
The number of bench-presses is 88.1 if the weight is 0
The correlation is r = −.9899, which represents a strongly correlated negative slope
The max number of bench-presses at 100 lbs. is 46.1 presses.
8a.
8b.
8c.
8d.
Y = .1478x + 11.5212
The slope is .1478, which represents increase in millions of visitors coming to the US per year.
.61219 = moderate correlation
The expected number of visitors in 2015 is 15.6596 million in 2015
AFM Unit 1 Review
Name_________________________________________
1. The following chart gives 𝑛 = 𝑓 (𝐴), which represents the number of gallons of paint needed to cover
the area 𝐴.
A
n
0
0
250
1
500
2
750
3
1000
4
1250
5
a.
Identify which is the independent and which is the dependent variable
b.
State the domain and range
c.
Is the relation depicted in the chart linear? If so, find the equation. If not, why?
1500
6
2. The population of four different towns, 𝑃𝐴 , 𝑃𝐵 , 𝑃𝐶 , 𝑃𝐷 are given by the following formulas where 𝑡 is
the year:
𝑃𝐴 = 10,000 + 1800𝑡
𝑃𝐵 = 55,000 – 300𝑡
𝑃𝐶 = 10,000 + 1800𝑡
𝑃𝐷 = 55,000 – 300𝑡
a.
which populations are represented by linear functions
b.
when do towns A and B have the same populations?
c.
describe in words what each linear model tells you about the population for town A and town B
AFM Unit 1 Review
Name_________________________________________
3. The table below gives the cost, 𝐶(𝑛), of producing computers as a linear function of 𝑛, the number of
units produced.
n (units)
100
125
150
175
C(n) (dollars)
11000
11125
11250
11375
a.
Find the 𝐶(120). Interpret your results.
b.
The fixed cost of production is the cost incurred before any goods are produced. The unit cost is
the cost of producing each unit. Find the fixed cost and unit cost for producing the computers.
Interpret your results.
4. The cost of a Frigbox refrigerator is $1150 and it depreciates $50 per year. The cost of an Artic
refrigerator is $1800 and depreciates $100 per year.
a.
If both refrigerators continue to depreciate at the rates given above, which has the higher value
after 8 years? (assuming they are bought at the same time)
b.
When will the two refrigerators have equal value?
AFM Unit 1 Review
Name_________________________________________
5. You need to purchase a new computer printer. The cost of printer A is $80 and its Ink cartridges are
$30 each. The cost of printer B is $120 and its ink cartridges are $20 each. You estimate that you will
need new ink cartridges about once a month.
a.
Write equations for the total cost for printer A and its ink and for printer B and its ink, where t is
time in months.
b.
After how many months will the amount of money spent on each be equal?
6. Tell whether the tables are linear. If so find the equation.
a.
x
g(x)
0
50
100
100
300
150
600
200
1000
250
b.
x
F(x)
0
-1
4
2
12
8
24
17
40
29
60
44
AFM Unit 1 Review
Name_________________________________________
7. An athlete wanting to strengthen his cardiovascular system will bench-press
a weight, w as many times, N as possible. The data in the table shows the
relationship between N and w.
Weight w,
(pounds)
Max number
bench presses, N
140
150
160
170
29
25
22
16
a.
Use your calculator to find the equation of the linear regression.
b.
Interpret the slope in the context of the problem.
c.
Interpret the vertical intercept in the context of the problem.
d.
Interpret the correlation coefficient (r-value).
e.
According to the regression model, what is the maximum number of bench presses that an athlete
can make if they are working with a 100 lb. weight?
AFM Unit 1 Review
Name_________________________________________
8. The following table shows the number of overseas visitors to the United States
since 1987. (in millions) Let t = 0 represent 1987
Year
Visitors
Year
Visitors
1987
10.434
1992
11.819
1988
12.763
1993
12.024
1989
12.184
1994
12.542
1990
12.252
1995
12.933
a.
Use your calculator to find the equation of linear regression.
b.
Interpret the slope in the context of the problem.
c.
Interpret the correlation coefficient (r-value).
d.
Use your regression equation to predict the number of visitors in 2015.
1991
12.003
1996
12.909