1. ਕੋਸ਼ਿਸ਼ ਕਰੋ
2. m= 4−3 0−2 = 1 −2 =− 1 2; ਘਟ ਰਿਹਾ ਹੈ ਕਿਉਂਕਿ m<0.
3. m= 1,868−1,442 2,012−2,009 = 426 3 =142 ਲੋਕ ਪ੍ਰਤੀ ਸਾਲ
4. y−2=−2( x+2 ) ; y=−2x−2
5. y−0=−3( x−0 ); y=−3x
6. y=−7x+3
7. H( x )=0.5x+12.5
8. ਸੰਭਵ ਜਵਾਬਾਂ ਵਿੱਚ (−3,7), (−6,9), ਜਾਂ (−9,11) ਸ਼ਾਮਲ ਹਨ।
9. (16, 0)
10. ⓐ f(x)=2x
11. ⓑ g(x)=− 1 2 x
12. y=–13x+6
13. ⓐ (0,5)
14. ⓑ (5, 0)
15. ⓒ ਢਲਾਣ -1
16. ⓓ ਨਾ ਸਮਾਂਤਰ ਨਾ ਲੰਬਵਤ
17. ⓔ ਘਟਦਾ ਫਲਨ
18. ⓕ ਦਿੱਤੇ ਗਏ ਤਾਦਾਤਮਕ ਫਲਨ, ਇੱਕ ਉੱਪਰ ਵੱਲ ਫਲਿੱਪ (t-ਧੁਰੇ ਉੱਤੇ) ਕਰੋ ਅਤੇ 5 ਇਕਾਈਆਂ ਉੱਪਰ ਖਿਸਕਾਓ।
19. ⓐ C( x )=0.25x+25,000
20. ⓑ y-ਅੰਤਰਖੰਡ ( 0,25,000 ) ਹੈ। ਜੇ ਕੰਪਨੀ ਇੱਕ ਵੀ ਡੋਨਟ ਦਾ ਉਤਪਾਦਨ ਨਹੀਂ ਕਰਦੀ, ਤਾਂ ਵੀ ਉਨ੍ਹਾਂ ਨੂੰ $25,000 ਦਾ ਖਰਚਾ ਆਉਂਦਾ ਹੈ।
21. ⓐ 41,100
22. ⓑ 2020
23. 21.57 ਮੀਲ
54°F54°F
24. 150.871 ਅਰਬ ਗੈਲਨ; ਬਾਹਰਲੇ ਅਨੁਮਾਨ
2.1 Section Exercises
Terry starts at an elevation of 3000 feet and descends 70 feet per second.
3 miles per hour
d( t )=100−10t d( t )=100−10t
Yes.
No.
No.
No.
Increasing.
Decreasing.
Decreasing.
Increasing.
Decreasing.
3
–13–13
4545
f(x)=−12x+72f(x)=−12x+72
y=2x+3y=2x+3
y=−13x+223y=−13x+223
y=45x+4y=45x+4
−54−54
y= 2 3 x+1 y= 2 3 x+1
y=−2x+3 y=−2x+3
y=3 y=3
Linear, g(x)=−3x+5g(x)=−3x+5
Linear, f(x)=5x−5f(x)=5x−5
Linear, g(x)=−252x+6g(x)=−252x+6
Linear, f(x)=10x−24f(x)=10x−24
f(x)=−58x+17.3 f(x)=−58x+17.3
a. a=11,900a=11,900; b=1000.1b=1000.1 b. q(p)=1000p−100q(p)=1000p−100
x=−163x=−163
x=ax=a
y=dc−ax−adc−ay=dc−ax−adc−a
$45 per training session.
The rate of change is 0.1. For every additional minute talked, the monthly charge increases by $0.1 or 10 cents. The initial value is 24. When there are no minutes talked, initially the charge is $24.
The slope is −400.−400. This means for every year between 1960 and 1989, the population dropped by 400 per year in the city.
c.
2.2 Section Exercises
The slopes are equal; y-intercepts are not equal.
The point of intersection is (a,a).(a,a). This is because for the horizontal line, all of the yy coordinates are aa and for the vertical line, all of the xx coordinates are a.a. The point of intersection will have these two characteristics.
First, find the slope of the linear function. Then take the negative reciprocal of the slope; this is the slope of the perpendicular line. Substitute the slope of the perpendicular line and the coordinate of the given point into the equation y=mx+by=mx+b and solve for b.b. Then write the equation of the line in the form y=mx+by=mx+b by substituting in mm and b.b.
neither parallel or perpendicular
perpendicular
parallel
(–2, 0)(–2, 0); (0, 4)(0, 4)
(15, 0)(15, 0); (0, 1)(0, 1)
(8, 0)(8, 0); (0, 28)(0, 28)
Line 1:m=8 Line 1:m=8Line 2:m=–6Line 2:m=–6Neither Neither
Line 1:m=– 1 2 Line 1:m=– 1 2 Line 2:m=2Line 2:m=2Perpendicular Perpendicular
Line 1:m=–2 Line 1:m=–2Line 2:m=–2Line 2:m=–2Parallel Parallel
g(x)=3x−3g(x)=3x−3
p(t)=−13t+2p(t)=−13t+2
(−2,1)(−2,1)
(−175,53)(−175,53)
F
C
A
ⓐ g(x)=0.75x−5.5g(x)=0.75x−5.5
ⓑ 0.75
ⓒ (0,−5.5)(0,−5.5)
y=3y=3
x=−3x=−3
no point of intersection
(2, 7) (2, 7)
(–10, –5)(–10, –5)
y=100x−98 y=100x−98
x< 1999 201 x> 1999 201 x< 1999 201 x> 1999 201
Less than 3000 texts
2.3 Section Exercises
Determine the independent variable. This is the variable upon which the output depends.
To determine the initial value, find the output when the input is equal to zero.
6 square units
20.012 square units
2,300
64,170
P( t )=75,000+2,500t P( t )=75,000+2,500t
(–30, 0) Thirty years before the start of this model, the town had no citizens. (0, 75,000) Initially, the town had a population of 75,000.
Ten years after the model began.
W( t )=0.5t+7.5 W( t )=0.5t+7.5
( −15,0 ) ( −15,0 ): The x-intercept is not a plausible set of data for this model because it means the baby weighed 0 pounds 15 months prior to birth. ( 0, 7.5 ) ( 0, 7.5 ): The baby weighed 7.5 pounds at birth.
At age 5.8 months.
C( t )=12,025−205t C( t )=12,025−205t
(58.7, 0) (58.7, 0): In roughly 59 years, the number of people inflicted with the common cold would be 0. (0,12,025) (0,12,025): Initially there were 12,025 people afflicted by the common cold.
2064
y=−2t+180 y=−2t+180
In 2070, the company’s profit will be zero.
y=30t−300 y=30t−300
(10, 0) In 1990, the profit earned zero profit.
Hawaii
During the year 1933
$105,620
ⓐ 696 people
ⓑ 4 years
ⓒ 174 people per year
ⓓ 305 people
ⓔ P(t)=305+174t P(t)=305+174t
ⓕ 2,219 people
ⓐ C( x )=0.15x+10 C( x )=0.15x+10
ⓑ The flat monthly fee is $10 and there is an additional $0.15 fee for each additional minute used
ⓒ $113.05
ⓐ P( t )=190t+4,360 P( t )=190t+4,360
ⓑ 6,640 moose
ⓐ R( t )=16−2.1t R( t )=16−2.1t
ⓑ 5.5 billion cubic feet
ⓒ During the year 2017
More than 133 minutes
More than $42,857.14 worth of jewelry
$66,666.67
2.4 Section Exercises
When our model no longer applies, after some value in the domain, the model itself doesn’t hold.
We predict a value outside the domain and range of the data.
The closer the number is to 1, the less scattered the data, the closer the number is to 0, the more scattered the data.
61.966 years
No.
No.
Interpolation. About 60° F. 60° F.
C
B
Yes, trend appears linear because r=0.985r=0.985 and will exceed 12,000 near midyear, 2016, 24.6 years since 1992.
y=1.640x+13.800y=1.640x+13.800, r=0.987r=0.987
y=−0.962x+26.86,r=−0.965 y=−0.962x+26.86,r=−0.965
y=−1.981x+60.197y=−1.981x+60.197; r=−0.998r=−0.998
y=0.121x−38.841,r=0.998y=0.121x−38.841,r=0.998
(−2,−6),(1,−12),(5,−20),(6,−22),(9,−28)(−2,−6),(1,−12),(5,−20),(6,−22),(9,−28); y=−2x−10y=−2x−10
(189.8,0)(189.8,0) If 18,980 units are sold, the company will have a profit of zero dollars.
y=0.00587x+1985.41y=0.00587x+1985.41
y=20.25x−671.5y=20.25x−671.5
y=−10.75x+742.50y=−10.75x+742.50
Review Exercises
Yes
Increasing.
y=−3x+26y=−3x+26
3
y=2x−2y=2x−2
Not linear.
parallel
(–9,0);(0,–7)(–9,0);(0,–7)
Line 1: m=−2;m=−2; Line 2: m=−2;m=−2; Parallel
y=−0.2x+21y=−0.2x+21
250.
118,000.
y=−300x+11,500y=−300x+11,500
a) 800; b) 100 students per year; c) P(t)=100t+1700P(t)=100t+1700
18,500
$91,625
Extrapolation.
Midway through 2024.
y=−1.294x+49.412;r=−0.974y=−1.294x+49.412;r=−0.974
Early in 2022
7,660
Practice Test
Yes.
Increasing
y=−1.5x−6y=−1.5x−6
y=−2x−1y=−2x−1
No.
Perpendicular
(−7,0)(−7,0); (0,−2)(0,−2)
y=−0.25x+12y=−0.25x+12
150
165,000
y=875x+10,675y=875x+10,675
a) 375; b) dropped an average of 46.875, or about 47 people per year; c) y=−46.875t+1250y=−46.875t+1250
Early in 2018
y=0.00455x+1979.5y=0.00455x+1979.5
r=0.999r=0.999