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If the function P is graphed, find and interpret the slope of the function.

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When will the population reach 100,000?

Ten years after the model began

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What is the population in the year 12 years from the onset of the model?

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For the following exercises, consider this scenario: The weight of a newborn is 7.5 pounds. The baby gained one-half pound a month for its first year.

Find the linear function that models the baby’s weight W as a function of the age of the baby, in months, t .

W ( t ) = 0.5 t + 7.5

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Find a reasonable domain and range for the function W .

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If the function W is graphed, find and interpret the x - and y -intercepts.

( 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 ) : The baby weighed 7.5 pounds at birth.

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If the function W is graphed, find and interpret the slope of the function.

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When did the baby weight 10.4 pounds?

At age 5.8 months

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What is the output when the input is 6.2?

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For the following exercises, consider this scenario: The number of people afflicted with the common cold in the winter months steadily decreased by 205 each year from 2005 until 2010. In 2005, 12,025 people were inflicted.

Find the linear function that models the number of people inflicted with the common cold C as a function of the year, t .

C ( t ) = 12 , 025 205 t

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Find a reasonable domain and range for the function C .

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If the function C is graphed, find and interpret the x - and y -intercepts.

( 58 . 7 , 0 ) : In roughly 59 years, the number of people inflicted with the common cold would be 0. ( 0 , 12 , 0 25 ) Initially there were 12,025 people afflicted by the common cold.

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If the function C is graphed, find and interpret the slope of the function.

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When will the output reach 0?

2063

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In what year will the number of people be 9,700?

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Graphical

For the following exercises, use the graph in [link] , which shows the profit, y , in thousands of dollars, of a company in a given year, t , where t represents the number of years since 1980.

Graph of a decreasing line from (15, 150) to (25, 130).  The x-axis goes from 0 to 30 in intervals of 5 and the y-axis goes from 125 to 155 in intervals of 5.

Find the linear function y , where y depends on t , the number of years since 1980.

y = 2 t +180

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Find and interpret the y -intercept.

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Find and interpret the x -intercept.

In 2070, the company’s profit will be zero.

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Find and interpret the slope.

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For the following exercises, use the graph in [link] , which shows the profit, y , in thousands of dollars, of a company in a given year, t , where t represents the number of years since 1980.

Graph of a line from (15, 150) to (25, 450).  The x-axis goes from 0 to 30 in intervals of 5 and the y-axis goes from 0 to 500 in intervals of 50.

Find the linear function y , where y depends on t , the number of years since 1980.

y = 3 0 t 3 00

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Find and interpret the y -intercept.

( 0 , 300 ) ; In 1980, the company lost $300,000.

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Find and interpret the x -intercept.

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Find and interpret the slope.

y = 30 t 300 of form y = m x + b , m = 30.

For each year after 1980, the company's profits increased $30,000 per year

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Numeric

For the following exercises, use the median home values in Mississippi and Hawaii (adjusted for inflation) shown in [link] . Assume that the house values are changing linearly.

Year Mississippi Hawaii
1950 $25,200 $74,400
2000 $71,400 $272,700

In which state have home values increased at a higher rate?

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Questions & Answers

How look for the general solution of a trig function
collins Reply
stock therom F=(x2+y2) i-2xy J jaha x=a y=o y=b
Saurabh Reply
root under 3-root under 2 by 5 y square
Himanshu Reply
The sum of the first n terms of a certain series is 2^n-1, Show that , this series is Geometric and Find the formula of the n^th
amani Reply
cosA\1+sinA=secA-tanA
Aasik Reply
why two x + seven is equal to nineteen.
Kingsley Reply
The numbers cannot be combined with the x
Othman
2x + 7 =19
humberto
2x +7=19. 2x=19 - 7 2x=12 x=6
Yvonne
because x is 6
SAIDI
what is the best practice that will address the issue on this topic? anyone who can help me. i'm working on my action research.
Melanie Reply
simplify each radical by removing as many factors as possible (a) √75
Jason Reply
how is infinity bidder from undefined?
Karl Reply
what is the value of x in 4x-2+3
Vishal Reply
give the complete question
Shanky
4x=3-2 4x=1 x=1+4 x=5 5x
Olaiya
hi can you give another equation I'd like to solve it
Daniel
what is the value of x in 4x-2+3
Olaiya
if 4x-2+3 = 0 then 4x = 2-3 4x = -1 x = -(1÷4) is the answer.
Jacob
4x-2+3 4x=-3+2 4×=-1 4×/4=-1/4
LUTHO
then x=-1/4
LUTHO
4x-2+3 4x=-3+2 4x=-1 4x÷4=-1÷4 x=-1÷4
LUTHO
A research student is working with a culture of bacteria that doubles in size every twenty minutes. The initial population count was  1350  bacteria. Rounding to five significant digits, write an exponential equation representing this situation. To the nearest whole number, what is the population size after  3  hours?
David Reply
v=lbh calculate the volume if i.l=5cm, b=2cm ,h=3cm
Haidar Reply
Need help with math
Peya
can you help me on this topic of Geometry if l help you
litshani
( cosec Q _ cot Q ) whole spuare = 1_cosQ / 1+cosQ
Aarav Reply
A guy wire for a suspension bridge runs from the ground diagonally to the top of the closest pylon to make a triangle. We can use the Pythagorean Theorem to find the length of guy wire needed. The square of the distance between the wire on the ground and the pylon on the ground is 90,000 feet. The square of the height of the pylon is 160,000 feet. So, the length of the guy wire can be found by evaluating √(90000+160000). What is the length of the guy wire?
Maxwell Reply
the indicated sum of a sequence is known as
Arku Reply

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Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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