Hello there. To solve this question, we'll have to set up an equation for each of the situations below.
a) The pay P for t hours at $17 an hour.
For this, we have a function P of t, that is, the pay depends on the number t of hours worked.
We can find the function by simply multiplying the pay for an hour by the number of hours, that is
[tex]P(t)=17t[/tex]
This is the answer contained in the option C).
b) The total pay P for a day of t working hours on which you charge a base rate of $32 and $14 for each hour worked.
In this case, again we multiply the number of hours worked by the cost for each hour and add $32, therefore
[tex]P(t)=14t+32[/tex]
This is the answer contained in the option A).
c) The total pay P for t hours at $22 and $16 for each additional hour.
In this case, we multiply 22 by the first hour, in this case, 1 and add it to 16 multiplied by (t - 1), that is, when t = 1, you get 0, that is, P = 22, therefore
[tex]P(t)=22+16\cdot(t-1)[/tex]
This is the answer contained in the option D.
