4.1 Linear Functions
Possible answers include or
4.2 Modeling with Linear Functions
a.b. The y-intercept isIf the company does not produce a single doughnut, they still incur a cost of $25,000.
4.1 Section Exercises
Terry starts at an elevation of 3000 feet and descends 70 feet per second.
The point of intersection isThis is because for the horizontal line, all of thecoordinates areand for the vertical line, all of thecoordinates areThe point of intersection is on both lines and therefore will have these two characteristics.
Line 1: m = –10 Line 2: m = –10 Parallel
Line 1: m = –2 Line 2: m = 1 Neither
69. $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. this means for every year between 1960 and 1989, the population dropped by 400 per year in the city.
4.2 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
20.01 square units
(–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
: 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.: The baby weighed 7.5 pounds at birth.
At age 5.8 months
In roughly 59 years, the number of people inflicted with the common cold would be 0.Initially there were 12,025 people afflicted by the common cold.
In 2070, the company’s profit will be zero.
(10, 0) In the year 1990, the company’s profits were zero
During the year 1933
- 696 people
- 4 years
- 174 people per year
- 305 people
- P(t) = 305 + 174t
- 2,219 people
- C(x) = 0.15x + 10
- The flat monthly fee is $10 and there is a $0.15 fee for each additional minute used
P(t) = 190t + 4,360
- R(t)= −2.1t + 16
- 5.5 billion cubic feet
- During the year 2017
More than 133 minutes
More than $42,857.14 worth of jewelry
More than $66,666.67 in sales
4.3 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.
Yes, trend appears linear becauseand will exceed 12,000 near midyear, 2016, 24.6 years since 1992.
Yes, the function is a good fit.
If 18,980 units are sold, the company will have a profit of zero dollars.
Line 1:Line 2:Parallel
More than 250
a) 800 b) 100 students per year c)
y = −1.5x − 6
y = −2x − 1
(−7, 0); (0, −2)
y = −0.25x + 12
Slope = −1 and y-intercept = 6
y = 875x + 10,625
- dropped an average of 46.875, or about 47 people per year
- y = −46.875t + 1250
In early 2018
y = 0.00455x + 1979.5
r = 0.999