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? a. 70% b. -27% c. -17% d. -75%

Answer 1

if the industry is losing 1.7 thousands jobs in one year, in 10 years it will then lose 1.7*10, or 17 thousand jobs.

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

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

solve for "x", round it up, make it negative, since it should be a negative rate, since is a decrease in the initial amount.

Answer 2

Using linear function concepts, it is found that the industry’s percent change from 2008 to 2018 will be of:

b. -27%

What is a linear function?

A linear function is modeled by:

$y = mx + b$

In which:

• m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

• b is the y-intercept, which is the value of y when x = 0.

In this problem:

• The industry had 63.1 thousand jobs in 2008, hence b = 63.1.

• This number is expected to decline at an average annual rate of 1.7 thousand jobs per year from 2008 to 2018, hence m = -1.7.

Thus, the function is:

y = -1.7x + 63.1.

In 2018, which is 10 years after 2008, the value of the function is:

y(10) = -1.7(10) + 63.1 = 46.1.

The percent change is given by the change divided by the initial value, hence:

(46.1 - 63.1)/63.1 = -27%

Hence option b is correct.

More can be learned about linear function concepts at https://brainly.com/question/24808124