QuestionFind the first year when percent change in beer shipments reaches $-34\%$ using $y=-4.1x+28.7$ . What does $-34\%$ represent? A. Slope B. $x$ C. $y$ D. $y$ -intercept.

Studdy Solution

STEP 1

Assumptions1. The percent change in beer shipments since the year2007 for a beer company can be approximated by $y=-4.1 x+28.7$ . . In this equation, $x=7$ corresponds to the year2007.
3. The model remains accurate.

STEP 2

The value $-34 \%$ represents the variable $y$ in the given equation, which is the percent change in beer shipments. So, we need to solve the equation for $x$ when $y=-34$ .

STEP 3

Set $y$ to $-34$ in the equation and solve for $x$ .
$-34 = -.1x +28.7$

STEP 4

Subtract $28.7$ from both sides of the equation to isolate the term with $x$ .
$-34 -28.7 = -4.1x$

STEP 5

Calculate the left side of the equation.
$-62.7 = -4.1x$

STEP 6

Divide both sides of the equation by $-4.1$ to solve for $x$ .
$x = \frac{-62.}{-4.1}$

STEP 7

Calculate the value of $x$ .
$x = \frac{-62.7}{-4.1} =15.29$

STEP 8

Since $x=7$ corresponds to the year2007, $x=15.29$ corresponds to the year $2007 +15.29 =2022.29$ .

STEP 9

Since we are looking for the first full year, we need to round $2022.29$ up to the nearest whole number, which is $2023$ .
The first full year in which the percent change reaches $-34 \%$ is2023.

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QuestionFind the first year when percent change in beer shipments reaches $-34\%$ using $y=-4.1x+28.7$ . What does $-34\%$ represent? A. Slope B. $x$ C. $y$ D. $y$ -intercept.

Studdy Solution

STEP 1

Assumptions1. The percent change in beer shipments since the year2007 for a beer company can be approximated by $y=-4.1 x+28.7$ . . In this equation, $x=7$ corresponds to the year2007.
3. The model remains accurate.

STEP 2

The value $-34 \%$ represents the variable $y$ in the given equation, which is the percent change in beer shipments. So, we need to solve the equation for $x$ when $y=-34$ .

STEP 3

Set $y$ to $-34$ in the equation and solve for $x$ .
$-34 = -.1x +28.7$

STEP 4

Subtract $28.7$ from both sides of the equation to isolate the term with $x$ .
$-34 -28.7 = -4.1x$

STEP 5

Calculate the left side of the equation.
$-62.7 = -4.1x$

STEP 6

Divide both sides of the equation by $-4.1$ to solve for $x$ .
$x = \frac{-62.}{-4.1}$

STEP 7

Calculate the value of $x$ .
$x = \frac{-62.7}{-4.1} =15.29$

STEP 8

Since $x=7$ corresponds to the year2007, $x=15.29$ corresponds to the year $2007 +15.29 =2022.29$ .

STEP 9

Since we are looking for the first full year, we need to round $2022.29$ up to the nearest whole number, which is $2023$ .
The first full year in which the percent change reaches $-34 \%$ is2023.

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QuestionFind the first year when percent change in beer shipments reaches −34%-34\%−34% using y=−4.1x+28.7y=-4.1x+28.7y=−4.1x+28.7. What does −34%-34\%−34% represent? A. Slope B. xxx C. yyy D. yyy-intercept.

Studdy Solution

STEP 1

Assumptions1. The percent change in beer shipments since the year2007 for a beer company can be approximated by y=−4.1x+28.7y=-4.1 x+28.7y=−4.1x+28.7. . In this equation, x=7x=7x=7 corresponds to the year2007.3. The model remains accurate.

STEP 2

The value −34%-34 \%−34% represents the variable yyy in the given equation, which is the percent change in beer shipments. So, we need to solve the equation for xxx when y=−34y=-34y=−34.

STEP 3

Set yyy to −34-34−34 in the equation and solve for xxx.−34=−.1x+28.7-34 = -.1x +28.7−34=−.1x+28.7

STEP 4

Subtract 28.728.728.7 from both sides of the equation to isolate the term with xxx.−34−28.7=−4.1x-34 -28.7 = -4.1x−34−28.7=−4.1x

STEP 5

Calculate the left side of the equation.−62.7=−4.1x-62.7 = -4.1x−62.7=−4.1x

STEP 6

Divide both sides of the equation by −4.1-4.1−4.1 to solve for xxx.x=−62.−4.1x = \frac{-62.}{-4.1}x=−4.1−62.​

STEP 7

Calculate the value of xxx.x=−62.7−4.1=15.29x = \frac{-62.7}{-4.1} =15.29x=−4.1−62.7​=15.29

STEP 8

Since x=7x=7x=7 corresponds to the year2007, x=15.29x=15.29x=15.29 corresponds to the year 2007+15.29=2022.292007 +15.29 =2022.292007+15.29=2022.29.

STEP 9

Since we are looking for the first full year, we need to round 2022.292022.292022.29 up to the nearest whole number, which is 202320232023.The first full year in which the percent change reaches −34%-34 \%−34% is2023.

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QuestionFind the first year when percent change in beer shipments reaches $-34\%$ using $y=-4.1x+28.7$ . What does $-34\%$ represent? A. Slope B. $x$ C. $y$ D. $y$ -intercept.

Assumptions1. The percent change in beer shipments since the year2007 for a beer company can be approximated by $y=-4.1 x+28.7$ . . In this equation, $x=7$ corresponds to the year2007.
3. The model remains accurate.

The value $-34 \%$ represents the variable $y$ in the given equation, which is the percent change in beer shipments. So, we need to solve the equation for $x$ when $y=-34$ .

Set $y$ to $-34$ in the equation and solve for $x$ .
$-34 = -.1x +28.7$

Subtract $28.7$ from both sides of the equation to isolate the term with $x$ .
$-34 -28.7 = -4.1x$

Calculate the left side of the equation.
$-62.7 = -4.1x$

Divide both sides of the equation by $-4.1$ to solve for $x$ .
$x = \frac{-62.}{-4.1}$

Calculate the value of $x$ .
$x = \frac{-62.7}{-4.1} =15.29$

Since $x=7$ corresponds to the year2007, $x=15.29$ corresponds to the year $2007 +15.29 =2022.29$ .

Since we are looking for the first full year, we need to round $2022.29$ up to the nearest whole number, which is $2023$ .
The first full year in which the percent change reaches $-34 \%$ is2023.