Question

Say a certain manufacturing industry has 63.1 thousand jobs in 2008, but is expected to decline at an average annual rate of 1.7 thousand jobs per year from 2008 to 2018. Assuming this holds true, what will be this industry’s percent change from 2008 to 2018?

Answer 1

well, in 10 years, from 2008 to 2018 at 1.7 thousands yearly, that means 1.7* 10, or 17 thousands.

so, if we take the 63.1 to be the 100%, how much is 17 off of it in percentage?


`\bf \begin{array}{ccllll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 63.1&100\\ 17&x \end{array}\implies \cfrac{63.1}{17}=\cfrac{100}{x}\implies x=\cfrac{17\cdot 100}{63.1}`

Answer 2

The industry’s percent change from 2008 to 2018 is 27.09%.

Explanation:

Jobs during the year of 2008 = 63.1 thousands

Average annual rate of 1.7 thousand jobs per year from 2008 to 2018

Jobs decline during 1 year = 1.7 thousands

Number of jobs during the period of 2008 to 2018 that is in 10 years

Number of jobs in 2018 years =

63.1 thousand - 10 years × 1.7 thousand/year=46 thousands

`\%change=\frac{\text{Jobs in 2008}-\text{Jobs in 2018}}{\text{Jobs in 2008}}*100`

`\%change=(63.1 thousands-46 thousands)/(63.1 thousands)* 100=27.09\%`

The industry’s percent change from 2008 to 2018 is 27.09%.