QuestionA manufacturing industry had 63.1k jobs in 2008, declining by 1.7k/year. What is the percent change by 2018? A) 70% B) -27% C) -17% D) -75%

Studdy Solution

STEP 1

Assumptions1. The industry has63.1 thousand jobs in2008. The industry is expected to decline at an average annual rate of1.7 thousand jobs per year from2008 to20183. We are calculating the percent change from2008 to2018

STEP 2

First, we need to calculate the total loss of jobs over the10-year period. We can do this by multiplying the annual rate of decline by the number of years.
$Total\, job\, loss = Annual\, rate\, of\, decline \\times Number\, of\, years$

STEP 3

Now, plug in the given values for the annual rate of decline and the number of years to calculate the total job loss.
$Total\, job\, loss =1.7\, thousand\, jobs/year \\times10\, years$

STEP 4

Calculate the total job loss.
$Total\, job\, loss =1.7\, thousand\, jobs/year \\times10\, years =17\, thousand\, jobs$

STEP 5

Now that we have the total job loss, we can calculate the percent change. The percent change is calculated by dividing the change in value by the original value, and then multiplying by100 to convert to a percentage.
$Percent\, change = \frac{Change\, in\, value}{Original\, value} \\times100\%$

STEP 6

In this case, the change in value is the total job loss, and the original value is the number of jobs in2008. Plug in these values to calculate the percent change.
$Percent\, change = \frac{17\, thousand\, jobs}{63.1\, thousand\, jobs} \\times100\%$

STEP 7

Calculate the percent change.
$Percent\, change = \frac{17\, thousand\, jobs}{63.1\, thousand\, jobs} \\times100\% = -26.9\%$ The percent change is approximately -27%, so the correct answer is B.

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QuestionA manufacturing industry had 63.1k jobs in 2008, declining by 1.7k/year. What is the percent change by 2018? A) 70% B) -27% C) -17% D) -75%

Studdy Solution

STEP 1

Assumptions1. The industry has63.1 thousand jobs in2008. The industry is expected to decline at an average annual rate of1.7 thousand jobs per year from2008 to20183. We are calculating the percent change from2008 to2018

STEP 2

First, we need to calculate the total loss of jobs over the10-year period. We can do this by multiplying the annual rate of decline by the number of years.
$Total\, job\, loss = Annual\, rate\, of\, decline \\times Number\, of\, years$

STEP 3

Now, plug in the given values for the annual rate of decline and the number of years to calculate the total job loss.
$Total\, job\, loss =1.7\, thousand\, jobs/year \\times10\, years$

STEP 4

Calculate the total job loss.
$Total\, job\, loss =1.7\, thousand\, jobs/year \\times10\, years =17\, thousand\, jobs$

STEP 5

Now that we have the total job loss, we can calculate the percent change. The percent change is calculated by dividing the change in value by the original value, and then multiplying by100 to convert to a percentage.
$Percent\, change = \frac{Change\, in\, value}{Original\, value} \\times100\%$

STEP 6

In this case, the change in value is the total job loss, and the original value is the number of jobs in2008. Plug in these values to calculate the percent change.
$Percent\, change = \frac{17\, thousand\, jobs}{63.1\, thousand\, jobs} \\times100\%$

STEP 7

Calculate the percent change.
$Percent\, change = \frac{17\, thousand\, jobs}{63.1\, thousand\, jobs} \\times100\% = -26.9\%$ The percent change is approximately -27%, so the correct answer is B.

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QuestionA manufacturing industry had 63.1k jobs in 2008, declining by 1.7k/year. What is the percent change by 2018? A) 70% B) -27% C) -17% D) -75%

Studdy Solution

STEP 1

Assumptions1. The industry has63.1 thousand jobs in2008. The industry is expected to decline at an average annual rate of1.7 thousand jobs per year from2008 to20183. We are calculating the percent change from2008 to2018

STEP 2

STEP 3

Now, plug in the given values for the annual rate of decline and the number of years to calculate the total job loss.Total job loss=1.7 thousand jobs/yeartimes10 yearsTotal\, job\, loss =1.7\, thousand\, jobs/year \\times10\, yearsTotaljobloss=1.7thousandjobs/yeartimes10years

STEP 4

Calculate the total job loss.Total job loss=1.7 thousand jobs/yeartimes10 years=17 thousand jobsTotal\, job\, loss =1.7\, thousand\, jobs/year \\times10\, years =17\, thousand\, jobsTotaljobloss=1.7thousandjobs/yeartimes10years=17thousandjobs

STEP 5

STEP 6

STEP 7

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Now, plug in the given values for the annual rate of decline and the number of years to calculate the total job loss.
$Total\, job\, loss =1.7\, thousand\, jobs/year \\times10\, years$

Calculate the total job loss.
$Total\, job\, loss =1.7\, thousand\, jobs/year \\times10\, years =17\, thousand\, jobs$