# 2.4 Fitting linear models to data  (Page 6/14)

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 $x$ $y$ 900 70 988 80 1000 82 1010 84 1200 105 1205 108

$y=0.\text{121}x-38.841,\text{\hspace{0.17em}}r=0.998$

## Extensions

Graph $f\left(x\right)=0.5x+10$ . Pick a set of 5 ordered pairs using inputs and use linear regression to verify that the function is a good fit for the data.

Graph $f\left(x\right)=-2x-10$ . Pick a set of 5 ordered pairs using inputs and use linear regression to verify the function.

$\left(\text{−2},-6\right),\left(\text{1},\text{−12}\right),\left(\text{5},\text{−2}0\right),\left(\text{6},\text{−22}\right),\left(\text{9},\text{−28}\right)$ ; $y=-2x-10$

For the following exercises, consider this scenario: The profit of a company decreased steadily over a ten-year span. The following ordered pairs shows dollars and the number of units sold in hundreds and the profit in thousands of over the ten-year span, (number of units sold, profit) for specific recorded years:

.

Use linear regression to determine a function $P$ where the profit in thousands of dollars depends on the number of units sold in hundreds.

Find to the nearest tenth and interpret the x -intercept.

If 18,980 units are sold, the company will have a profit of zero dollars.

Find to the nearest tenth and interpret the y -intercept.

## Real-world applications

For the following exercises, consider this scenario: The population of a city increased steadily over a ten-year span. The following ordered pairs shows the population and the year over the ten-year span, (population, year) for specific recorded years:

Use linear regression to determine a function $y,$ where the year depends on the population. Round to three decimal places of accuracy.

$y=0.00587x+\text{1985}.4\text{1}$

Predict when the population will hit 8,000.

For the following exercises, consider this scenario: The profit of a company increased steadily over a ten-year span. The following ordered pairs show the number of units sold in hundreds and the profit in thousands of over the ten year span, (number of units sold, profit) for specific recorded years:

.

Use linear regression to determine a function y , where the profit in thousands of dollars depends on the number of units sold in hundreds .

$y=\text{2}0.\text{25}x-\text{671}.\text{5}$

Predict when the profit will exceed one million dollars.

For the following exercises, consider this scenario: The profit of a company decreased steadily over a ten-year span. The following ordered pairs show dollars and the number of units sold in hundreds and the profit in thousands of over the ten-year span (number of units sold, profit) for specific recorded years:

Use linear regression to determine a function y , where the profit in thousands of dollars depends on the number of units sold in hundreds .

$y=-\text{1}0.\text{75}x+\text{742}.\text{5}0$

Predict when the profit will dip below the \$25,000 threshold.

## Linear Functions

Determine whether the algebraic equation is linear. $2x+3y=7$

Yes

Determine whether the algebraic equation is linear. $6{x}^{2}-y=5$

Determine whether the function is increasing or decreasing.

$f\left(x\right)=7x-2$

Increasing.

how fast can i understand functions without much difficulty
what is set?
a colony of bacteria is growing exponentially doubling in size every 100 minutes. how much minutes will it take for the colony of bacteria to triple in size
I got 300 minutes. is it right?
Patience
no. should be about 150 minutes.
Jason
It should be 158.5 minutes.
Mr
ok, thanks
Patience
100•3=300 300=50•2^x 6=2^x x=log_2(6) =2.5849625 so, 300=50•2^2.5849625 and, so, the # of bacteria will double every (100•2.5849625) = 258.49625 minutes
Thomas
what is the importance knowing the graph of circular functions?
can get some help basic precalculus
What do you need help with?
Andrew
how to convert general to standard form with not perfect trinomial
can get some help inverse function
ismail
Rectangle coordinate
how to find for x
it depends on the equation
Robert
yeah, it does. why do we attempt to gain all of them one side or the other?
Melissa
whats a domain
The domain of a function is the set of all input on which the function is defined. For example all real numbers are the Domain of any Polynomial function.
Spiro
Spiro; thanks for putting it out there like that, 😁
Melissa
foci (–7,–17) and (–7,17), the absolute value of the differenceof the distances of any point from the foci is 24.
difference between calculus and pre calculus?
give me an example of a problem so that I can practice answering
x³+y³+z³=42
Robert
dont forget the cube in each variable ;)
Robert
of she solves that, well ... then she has a lot of computational force under her command ....
Walter
what is a function?
I want to learn about the law of exponent
explain this