Let's tackle this question step by step.
### Part (a)
The coefficient [tex]\(0.13\)[/tex] in the function [tex]\(C = f(h) = 36.24 + 0.13h\)[/tex] represents the cost per additional kilowatt hour of electricity used beyond the first 250 kWh.
In other words, for every kilowatt hour (kWh) used over 250 kWh, the customer is charged an additional [tex]$0.13.
### Part (b)
To find \(f(57)\), let's evaluate the function \(f(h) = 36.24 + 0.13h\) at \(h = 57\).
Substituting \(h = 57\) into the function, we get:
\[ f(57) = 36.24 + 0.13 \times 57 \]
Simplifying this:
\[ f(57) = 36.24 + 7.41 \]
\[ f(57) = 43.65 \]
So, \(f(57) = 43.65\).
#### Interpretation:
This means that the total cost for a customer who uses 307 kWh of electricity in a month (which is 250 kWh plus an additional 57 kWh) is $[/tex]43.65.
### Filling in the interpretation:
[tex]\[ f(57) = 43.65 \][/tex]
This tells us that it costs [tex]$43.65 dollars when a customer uses 307 kWh of electricity in a month.
To summarize:
- The coefficient \(0.13\) means that it costs $[/tex]0.13 for each additional kilowatt hour of electricity used in excess of 250 kWh.
- When calculating [tex]\(f(57)\)[/tex], it reveals that the cost when a customer uses 307 kWh of electricity in a month is $43.65.
