The pipe fitting industry had 546.5 thousand jobs in 2015 and is expected to decline at an average rate of 3 thousand jobs per year from 2015 to 2025. Assuming this holds true, what will be the pipe fitting's percent change from 2015 to 2025

The amount of jobs from fitting industry shall decline in 5.5 percent from 2015 to 2025.

Step-by-step explanation:

Due to the assumption of a yearly average rate, a linear function model shall be used. The expected amount of jobs () after a certain amount of years (t) is given by the following formula:

Where:

- Initial amount of jobs in pipe fitting industry, measured in thousands.

- Average yearly rate, measured in thousands per year. (A decline is indicated by a negative sign)

If , and , then:

The percent change in jobs from pipe fitting industry is calculated as follows:

The amount of jobs from fitting industry shall decline in 5.5 percent from 2015 to 2025.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1