https://file.aiquickdraw.com/mathbot/file/172684035841068khhdju.jpg

Let's break down the question based on the image:

You are given the cost function for electricity:
\[ C(h) = 36.93 + 0.14h \]
where:
- $ C(h) $ represents the monthly cost of electricity,
- $ h $ is the number of kilowatt-hours (kWh) of electricity used in excess of 250 kWh.

### Part (a) - Interpretation of the coefficient 0.14:
The coefficient 0.14 is associated with the variable $ h $, which represents the number of kilowatt-hours (kWh) used beyond 250 kWh. Thus, it means that the cost per additional kilowatt-hour (kWh) beyond 250 kWh is **0.14 dollars**.

### Part (b) - Finding $ f(43) $ and interpreting its meaning:
In the second part, you are asked to find $ f(43) $, which represents the total cost when the customer uses 43 kWh in excess of 250 kWh.

Given:
\[
f(43) = 36.93 + 0.14 \times 43 = 36.93 + 6.02 = 42.95
\]
This shows that the monthly cost is **$42.95** when a customer uses **43 kWh** of electricity in excess of 250 kWh.

Does that help clarify the problem? Feel free to ask any further questions or for more details.

Here are some follow-up questions:

1. How would the cost change if the usage exceeds 100 kWh instead of 43 kWh?
2. What would be the total cost for using exactly 250 kWh?
3. If the energy rates increase, how would the coefficient 0.14 change?
4. Could you express the total cost for any number of kilowatt-hours above 250 kWh?
5. How would you set up a function for another energy provider with different service and per-kWh rates?

Tip: When interpreting coefficients in cost functions, remember that they often represent rates or unit costs (e.g., cost per kWh, cost per item, etc.).

Long Island Power Authority charges its residential customers a monthly service charge plus an energy charge based on the amount of electricity used. The monthly cost of electricity is approximated by the function: C(h) = 36.93 + 0.14h, where h represents the number of kilowatt hours (kWh) of electricity used in excess of 250 kWh.

(a) What does the coefficient 0.14 mean in terms of the cost of electricity?
(b) Find f(43) and interpret its meaning.

Learn how to interpret the cost function C(h) = 36.93 + 0.14h for electricity usage, where h represents kilowatt-hours used in excess of 250 kWh. We also calculate f(43) and explain its real-world meaning.

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