Electricity Rates in Florida Florida Power Light Company...

Electricity Rates in Florida Florida Power & Light Company supplies electricity to residential customers for a monthly customer charge of 8.01dollar plus 8.89 cents per kilowatt hour (kWh) for up to 1000 kilowatt hours. (a) Write a linear equation that relates the monthly charge $C$, in dollars, to the number $x$ of kilowatt hours used in a month, $0 \leq x \leq 1000$. (b) Graph this equation. (c) What is the monthly charge for using 200 kilowatt hours? (d) What is the monthly charge for using 500 kilowatt hours? (e) Interpret the slope of the line.

Electricity Rates in Florida Florida Power & Light Company supplies electricity to residential customers for a monthly customer charge of 8.01dollar plus 8.89 cents per kilowatt hour (kWh) for up to 1000 kilowatt hours.
(a) Write a linear equation that relates the monthly charge $C$, in dollars, to the number $x$ of kilowatt hours used in a month, $0 \leq x \leq 1000$.
(b) Graph this equation.
(c) What is the monthly charge for using 200 kilowatt hours?
(d) What is the monthly charge for using 500 kilowatt hours?
(e) Interpret the slope of the line.

Key Concepts

Linear Equation Modeling

This concept involves representing a relationship between two variables using a linear equation. In utility billing, a fixed fee combined with a variable rate per unit of consumption naturally forms a linear model that predicts the total cost based on usage.

Slope-Intercept Form

The slope-intercept form (y = mx + b) is a standard way of expressing linear equations, where 'b' is the constant term or fixed cost and 'm' is the slope representing the variable cost per unit. This form is essential in understanding and constructing accurate cost models.

Graphing Linear Functions

Graphing involves plotting the equation on a coordinate plane to visually represent the relationship between the two variables. In this context, the horizontal axis represents consumption, and the vertical axis represents the total charge, illustrating how charges increase linearly with usage.

Interpreting the Slope

The slope of a linear equation indicates the rate of change between the variables. In practical situations like billing, it shows the additional charge incurred for each additional unit of consumption, providing insight into how variable costs affect the overall cost.

Function Evaluation

This process involves substituting specific values for the independent variable into the equation to determine the corresponding output. It is a useful tool for calculating actual charges for specific usage amounts, thereby facilitating cost estimation based on consumption.

Transcript

00:01 We are going to do problem number 127.

00:04 What we have to do here in this case is we have to just write a equation that relates the total cost to a customer okay for electricity so let's say that charge is c and the amount of charge that if they have they must have to pay is 8 .01 so we have to write here 8 .01.

00:28 This is the fixed amount plus 8 .89 cents per hour per kilowatt hour so let's say x is the number of kilowatt hour and the amount paid is 8 .8 .9 cents to so to convert it in the dollar we have to write it like this 0 .0 889 cents okay we can write it just more clearly 0 .889 nine cents 0 .0 8 it would be because it is in cent 889 cent okay now this becomes the price this becomes the price that each customer have to pay have to pay okay and here x is a variable it means that how much they use they have to pay according to that as for that so this is the price that they need to pay now moving out to the next question this is answered to first part no in b part we have to just and grab this equation so for that we need coordinate okay so let's say this is x and this is y so an x is going to be zero c is going to be 8 .01 everything is in dollar now in c let's say when x is going to be one then this is going to be 8 .0989 okay 8 .0 9 8 .9 so let us just plot it here this is y x this is minus y x this is minus x let's say this is 0 and this is 1 okay this is 1 so when x is 0 y is 8 .0 1 let's say somewhere here this is 8 .01 and somewhere here this is 8 .0989 here.

02:52 So this is the first point and this is the second point.

02:58 So this is the graph that the customer equation.

03:03 Okay, this is the graph of this equation.

03:07 So we draw, we had to just round the graph now moving to the next part to the c part here so in c part monthly charge for 200 kilowatt hour so here in place of x we have to just place 200 0 .0 0889 into 200 plus 880 plus you have to just solve this here little bit of calculation is there so we have to just be little extra careful 0 .089 multiplied to 200 so this will charge them 17 .78 okay 17 .78 plus 8 .01 so this should be added to 8 .01 so this will give us 25 .79...

Please give Ace some feedback