Question

in 2018, there were approximately 744.8 thousand electricians in a large country, with demand for electricians expected to increase by 6.17 thousand each year.
a. assuming the number of electricians in 2018 represents the demand for that year, express the demand for electricians in the country, d, in thousands, as a function of the number of years after 2018, x.
b. if the demand increases as expected, during which year will demand for electricians in the country reach 800 thousand?
a. d(x) =
(simplify your answer. use integers or decimals for any numbers in the equation.)

Explanation:

Step1: Identify the initial value and rate of change

The initial demand in 2018 ($x = 0$) is $D(0)=744.8$ thousand and the rate of increase is $6.17$ thousand per year. The general form of a linear - function is $D(x)=mx + b$, where $m$ is the slope (rate of change) and $b$ is the y - intercept (initial value).

Step2: Write the function

Here, $m = 6.17$ and $b = 744.8$. So, $D(x)=6.17x + 744.8$.

Step3: Solve for $x$ when $D(x)=800$

Set $D(x)=800$, then $800=6.17x + 744.8$.
Subtract 744.8 from both sides: $800 - 744.8=6.17x$, so $55.2 = 6.17x$.
Divide both sides by 6.17: $x=\frac{55.2}{6.17}\approx9$.
Since $x$ represents the number of years after 2018, the year is $2018 + 9=2027$.

Answer:

a. $D(x)=6.17x + 744.8$
b. 2027