Question

The charge of an electrician includes the cost of materials for the work to be done plus labour charges per hour and also the tax on cost of material. A work take h hours to complete. Now the total cost is given by function B(h) = 47h + 2.88 + 72, then the term 47h represents.
$\begin{align}
  & \text{a) the hourly rate} \\
 & \text{b) the site visit fee} \\
 & \text{c) The cost of the materials, including tax} \\
 & \text{d) The cost of material not including tax} \\
\end{align}$

Answer 1

Hint: Now we are given that the total cost is given by B(h) = 47h + 2.88 + 72. The expression is a function In h where h is in hours. Rest two terms are constant. Now since the total cost includes labour charges per hour, tax on the cost of material and the cost of the material. Hence we can compare the two statements and find the meaning of 47h.

Complete step by step answer:
Now B(h) = 47h + 2.88 + 72 where B(h) is the total cost.
This is a function in h.
Let us understand first what a function means.
Now the function is nothing but an input-output system. We give value and then get a value in return.
Hence we have a variable in a function, we substitute different values of inputs in these variables and get different output.
For example let us consider a simple function defined as f(x) = x + 1.
Now here we can say that x is our variable. Hence for each different value of x we get an output f(x).
For x = 1 we have f(1) = 1 + 1 = 2
For x = 2 we have f(2) = 2 + 1 = 3.
Now consider the given function B(h) = 47h + 2.88 + 72
Here we can say that h is the variable, where h represents the number of hours
Now the function gives total cost.
Now the total cost is made of 3 expenses. The cost of materials, the tax on cost of material and labour charges per hour.
Now we know that the cost of material and tax are constant values. Only expense that may change with time is labour charges per hour.
Since the term 47h, also changes with time we can say that the term represents labour charges per hour.
Option a is the correct option.

Note:
 Now note that the function might not always have a variable. We can say that f(x) = 7. Is also a function such that it is called a constant function which means for all values of x the value of a function is 7. Now for a function, we can also have more than one variable.