Thread: Function Problem! College Algebra.

I worked out the rest of the questions, but I am stuck on what to do at the end.

The problem reads:

Julie needs to hire a plumber. She is told that the cost of hiring the plumber, C , is a function of time spent on the job, t , in hours. The plumber charges a one time fee of $60 and an hourly rate of $50.

The first question said "Determine a function which describes the total cost of hiring the plumber as a function of time"
and I put "C=60 + 50X"

So, the question that I am stuck on says

Find the Value for C(0).

...I did this

C(0) = 60 + 50x

0 = 60 + 50x

-60 = 50x

-6/5 = X

...Is this right? I ... have no idea what I am s'posed to plug 0 into.
I also tried

C(0) = 60 + 50(0)

C=60.

...The other questions are like

question2) If plumber took 2 hours, how much did he make?
c=60+50(2)
c=160$

question3)5 hours?
c=60+50(5)
c=310$

question4)
What if Julie paid him 210$?
210=60+50x
x=3 hrs.

We call C a function of time t hence we have

C(t) = 60+50t

You want to find C(0), so you put 0 instead of t into the function and get

C(t) = 60+50t => C(0) = 60+50*(0) = 60$

What you've done is calculating for which value of t in the function C(t) that gives us the value 0, or in mathematics C(t) = 0.

On the other questions for example, if the plumper took 2 hours, we have C(2)

C(t) = 60+50t => C(2) = 60+50*2 = 160$

And on Q4 we want to solve C(t) = 210

C(t) = 210 <=> 60+50t = 210 <=> t = 3 hours

Thank you!