Question

An electrician charges an initial fee of $50 and $190 after 4 hours of work
Write a linear model that represents the total cost as a function of the number of hours worked

Answer 1

Linear eq. as function of number  of time $f_{(t)} = 35t + 50$

Rate of service per hour $a = 35$

Explanation :

Let the number of hours $= t$

Total cost $= f_{(t)}$

Rate of per hours $= a$

Then the linear model will be $f_{(t)} = at + b$  

Where, $b = \textrm{initial fee}$ = it is the constant on y – axis.

 So the equation $190 = a \times 4 + 50$             $(\textrem{given, t} = 4$, $b = 50$ )                                

$a \times 4 = 190 - 50$

$a \times 4 = 140$

$a = \frac{140}{4}$

Rate of service per hour $a = 35$

Linear equation of service as function of number time $f_{(t)} = 35t + 50$