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QuestionFind the first full year when the percent change in beer shipments reaches −34%-34\% using y=−4.1x+28.7y=-4.1x+28.7. What does −34%-34\% mean?

Studdy Solution

STEP 1

Assumptions1. The percent change in beer shipments can be approximated by the equation y=−4.1x+28.7y=-4.1 x+28.7 . In this equation, x=7x=7 corresponds to the year20073. The model remains accurate over time4. We are looking for the first full year where the percent change reaches −34%-34 \%
5. The value −34%-34 \% represents the percent change in beer shipments

STEP 2

First, we need to find the value of xx when y=−34y=-34. We can do this by setting y=−34y=-34 in the given equation and solving for xx.
−34=−4.1x+28.7-34 = -4.1x +28.7

STEP 3

Rearrange the equation to solve for xx.
−.1x=−34−28.7-.1x = -34 -28.7

STEP 4

implify the right side of the equation.
−4.1x=−62.7-4.1x = -62.7

STEP 5

Divide both sides of the equation by −4.1-4.1 to solve for xx.
x=−62.7−4.1x = \frac{-62.7}{-4.1}

STEP 6

Calculate the value of xx.
x=−62.−4.1=15.29x = \frac{-62.}{-4.1} =15.29

STEP 7

Remember that x=7x=7 corresponds to the year2007. So, x=15.29x=15.29 corresponds to the year 2007+15.29=2022.292007 +15.29 =2022.29. Since we are looking for the first full year, we need to round up to the next whole number.
Year=2023Year =2023The first full year in which the percent change in beer shipments reaches −34%-34 \% is2023.

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